Meta tags:
keywords=Online Math Notes, Online Math Tutorial, Math Notes, Math Tutorial, Algebra Notes, Algebra Tutorial, Calculus Notes, Calculus Tutorial, Calc Notes, Calc Tutorial, Calc I Notes, Calc I Tutorial, Calculus I Notes, Calculus I Tutorial, Calc II Notes, Calc II Tutorial, Calculus II Notes, Calculus II Tutorial, Calc III Notes, Calc III Tutorial, Calculus III Notes, Calculus III Tutorial, Calc 1 Notes, Calc 1 Tutorial, Calculus 1 Notes, Calculus 1 Tutorial, Calc 2 Notes, Calc 2 Tutorial, Calculus 2 Notes, Calculus 2 Tutorial, Calc 3 Notes, Calc 3 Tutorial, Calculus 3 Notes, Calculus 3 Tutorial, Calculus Help, DE Notes, DE Tutorial, Differential Equations Notes, Differential Equations Tutorial, Differential Equations Help, Algebra Review, Trig Review, Algebra Cheat Sheet, Trig Cheat Sheet;
description=Welcome to my math notes site. Contained in this site are the notes (free and downloadable) that I use to teach Algebra, Calculus (I, II and III) as well as Differential Equations at Lamar University. The notes contain the usual topics that are taught in those courses as well as a few extra topics that I decided to include just because I wanted to. There are also a set of practice problems, with full solutions, to all of the classes except Differential Equations. In addition there is also a selection of cheat sheets available for download.;

Headings (most frequently used words):

math, calculus, notes, paul, online, class, cheat, sheets, tables, reviews, extras, algebra, 1314, 2413, ii, 2414, iii, 2415, differential, equations, 2320,

Text of the page (most frequently used words):
the (1989), will (1116), and (1005), this (950), section (751), equations (443), functions (359), that (346), for (337), also (304), how (282), integrals (255), #differential (249), with (242), function (242), discuss (238), series (231), give (224), are (219), can (184), look (184), some (180), chapter (154), two (149), derivatives (149), equation (147), used (138), solving (135), one (132), define (128), order (127), introduce (127), calculus (120), coordinates (116), use (115), vector (115), work (114), limits (113), systems (112), well (108), trig (104), laplace (101), using (101), not (100), variables (99), more (98), find (97), solve (97), solutions (93), method (92), partial (91), linear (91), examples (90), integral (90), applications (87), value (85), basic (83), solution (83), take (82), transforms (81), surface (81), problems (80), test (79), quick (79), process (79), which (78), theorem (77), you (76), form (75), three (75), dimensional (75), system (75), determine (74), these (72), show (72), many (70), area (69), line (68), rule (67), see (66), polar (66), all (65), several (65), definition (64), from (63), vectors (62), review (61), what (61), standard (61), derivative (61), properties (60), parametric (59), finding (59), have (58), rational (57), than (57), couple (56), exponential (56), graph (56), formulas (55), coordinate (55), into (55), common (54), given (54), first (54), second (52), very (52), looking (51), integration (51), inequalities (51), absolute (50), polynomials (50), definite (49), get (49), about (48), inverse (48), length (48), lines (48), curves (48), logarithm (48), algebra (47), topics (47), them (47), complex (46), higher (46), notation (46), only (45), roots (45), tangent (45), quadratic (45), between (45), they (45), useful (45), addition (45), formula (43), illustrate (42), derive (42), here (41), brief (41), important (41), included (40), arc (40), power (40), graphing (40), need (40), previous (40), allow (40), sections (39), general (39), techniques (39), points (39), when (38), eigenvalues (38), polynomial (38), involve (38), infinite (38), indefinite (37), math (36), class (36), numbers (35), fourier (35), double (35), spherical (35), including (35), space (35), start (35), course (34), involving (34), discussion (34), cartesian (34), most (33), particular (33), facts (33), differentiation (33), surfaces (33), change (33), substitution (33), there (32), concepts (32), computing (32), fields (32), both (32), compute (32), determining (32), boundary (31), normal (31), values (31), part (31), however (30), few (30), illustrating (30), overview (30), concept (30), always (30), axis (30), cases (29), cylindrical (29), often (28), solid (28), just (27), other (27), relative (27), methods (27), involved (26), students (26), matrix (26), homogeneous (26), graphs (26), where (26), independent (26), variety (26), much (26), really (26), region (26), terms (25), notes (25), product (25), convergence (25), limit (25), revolution (25), minimum (25), maximum (25), exponents (25), without (25), point (25), needed (25), errors (24), cover (24), planes (24), basics (24), any (24), real (24), regions (24), volume (24), bounded (24), acceleration (24), help (23), but (23), note (23), ideas (23), set (23), heat (23), solids (23), infinity (23), plane (22), fundamental (22), divergence (22), multiple (22), chain (22), root (22), example (22), able (22), kind (22), application (22), evaluate (22), variable (22), problem (21), down (21), triple (20), factoring (20), derivation (20), converge (20), frac (20), next (20), natural (20), converting (20), interval (20), curve (20), may (19), phase (19), equilibrium (19), sequences (19), comparison (19), taylor (19), mean (19), coefficients (18), variation (18), parameters (18), nonhomogeneous (18), improper (18), expressions (18), conditions (18), extension (18), right (18), object (18), integrating (18), continue (18), revisit (18), rate (18), covered (17), heaviside (17), working (17), rates (17), left (17), various (17), information (16), each (16), undetermined (16), radicals (16), material (16), convert (16), possible (16), repeated (16), now (16), while (16), sketch (16), simple (16), guidelines (16), alternate (16), velocity (16), idea (16), quickly (16), formally (16), rather (16), geometric (16), converges (16), diverges (16), proof (16), sequence (16), topic (15), type (15), logarithms (15), table (15), version (15), different (15), ivp (15), modeling (15), ratio (15), related (15), interpretations (15), implicit (15), nonlinear (15), constant (15), piecewise (15), then (15), their (15), know (15), over (15), extend (15), being (14), cheat (14), has (14), knowledge (14), curvature (14), fractions (14), zeroes (14), square (14), understand (14), classes (14), generally (14), sets (14), initial (14), transform (14), wronskian (14), portraits (14), relationship (14), field (14), answer (14), actually (14), interpretation (14), fact (14), diverge (14), tend (14), vertical (14), require (14), primer (13), does (13), introduction (13), arithmetic (13), occasion (13), time (13), wave (13), separation (13), orthogonal (13), sine (13), euler (13), dirac (13), delta (13), coefficient (13), gradient (13), fairly (13), average (13), critical (13), hyperbolic (13), symmetry (13), types (13), off (13), evaluation (13), detailed (12), pages (12), green (12), extrema (12), practice (12), circles (12), works (12), quite (12), pretty (12), going (12), times (12), characteristic (12), distinct (12), validity (12), direction (12), yet (12), saw (12), minimums (12), maximums (12), domain (12), quadric (12), products (12), horizontal (12), least (11), later (11), available (11), full (11), sheets (11), another (11), out (11), cosine (11), mechanical (11), conservative (11), differentials (11), iii (11), dot (11), alternating (11), probability (11), substitutions (11), decreasing (11), logarithmic (11), augmented (11), include (11), examine (11), forms (11), prior (10), number (10), binormal (10), tangents (10), parabolas (10), were (10), done (10), situations (10), sum (10), cos (10), sin (10), showing (10), intervals (10), already (10), every (10), definitions (10), linearly (10), approximation (10), did (10), matrices (10), dependent (10), nice (10), manipulation (10), move (10), concentrate (10), objects (10), identify (10), might (10), although (10), slope (10), level (10), cylinders (10), alternative (10), integer (10), approximate (10), absolutely (10), either (10), rotating (10), prove (10), study (9), written (9), non (9), little (9), way (9), intended (9), print (9), final (9), step (9), vibrations (9), exact (9), directional (9), cross (9), center (9), force (9), parts (9), approximating (9), increasing (9), quotient (9), sided (9), continuity (9), dividing (9), answers (9), lot (9), write (9), whether (9), discussed (9), main (9), our (9), understanding (9), last (8), site (8), assume (8), required (8), mostly (8), extras (8), same (8), tables (8), respect (8), optimization (8), ellipses (8), hyperbolas (8), don (8), your (8), words (8), summary (8), radius (8), zero (8), ordinary (8), situation (8), representing (8), limits_ (8), infty (8), occur (8), make (8), looked (8), difference (8), behind (8), chapters (8), differentiating (8), represent (8), lead (8), case (8), starting (8), unlike (8), great (8), taking (8), quantities (8), reduction (8), greater (8), depth (8), approximations (8), amount (8), factor (8), certain (8), changing (8), those (8), subtlety (8), briefly (8), around (8), must (8), tests (8), proofs (8), parameter (8), algebraic (8), concave (8), described (8), density (8), plate (8), called (8), summation (8), newton (8), hospital (8), tell (8), differentiate (8), asked (8), precise (8), angles (8), vital (8), degree (8), add (8), subtract (8), successful (8), page (7), aren (7), introduced (7), contain (7), new (7), needing (7), gives (7), circle (7), could (7), eigenfunctions (7), nonconstant (7), convolution (7), separable (7), stokes (7), curl (7), lagrange (7), multipliers (7), estimating (7), binomial (7), mass (7), hydrostatic (7), pressure (7), quadratics (7), elimination (7), completing (7), exponent (7), presented (7), put (7), hopefully (7), through (7), subject (7), etc (7), detail (7), typically (7), transformations (7), should (6), four (6), seen (6), adding (6), exactly (6), been (6), back (6), single (6), unit (6), assumed (6), such (6), learn (6), vibrating (6), string (6), would (6), fixed (6), temperature (6), terminology (6), rest (6), principle (6), superposition (6), solved (6), periodic (6), opposed (6), extensions (6), identical (6), simply (6), because (6), mixing (6), water (6), connected (6), spring (6), associated (6), wide (6), its (6), model (6), almost (6), population (6), bernoulli (6), throughout (6), behavior (6), come (6), special (6), summarize (6), original (6), setting (6), difficult (6), rings (6), constraints (6), run (6), dealing (6), traces (6), won (6), isn (6), scalar (6), wider (6), unfortunately (6), positive (6), obtained (6), rectangular (6), eliminating (6), resulting (6), finite (6), collectively (6), before (6), distance (6), devoted (6), business (6), marginal (6), allowing (6), raised (6), base (6), six (6), asymptotes (6), calculator (6), expression (6), division (6), multiply (6), trigonometry (6), anyone (5), complete (5), usually (5), still (5), currently (5), sized (5), piece (5), covers (5), think (5), eigenvectors (5), potential (5), tutorial (5), got (5), assignment (5), strategy (5), evaluating (5), shifts (5), composition (5), preliminaries (5), negative (5), under (5), wish (5), fast (5), apply (5), getting (5), doing (5), major (5), courses (5), intermediate (5), exponentials (5), paul (4), taken (4), originally (4), powers (4), versions (4), reduced (4), contains (4), front (4), paper (4), areas (4), background (4), option (4), online (4), tips (4), below (4), displacement (4), bar (4), instead (4), thin (4), applied (4), reduce (4), reminder (4), derivations (4), a_n (4), b_n (4), even (4), mutually (4), results (4), estimate (4), something (4), regular (4), basis (4), kinds (4), interesting (4), differences (4), extending (4), outside (4), develop (4), doesn (4), singular (4), construct (4), discussions (4), subtracting (4), nodes (4), after (4), saddle (4), formal (4), corresponding (4), term (4), known (4), try (4), restricted (4), ask (4), question (4), again (4), moving (4), engineering (4), theory (4), stable (4), physical (4), liquid (4), falling (4), identifying (4), thoughts (4), investigate (4), having (4), never (4), parameterization (4), third (4), needs (4), defined (4), revisited (4), disks (4), neither (4), thought (4), notations (4), nothing (4), whose (4), position (4), tangential (4), early (4), concentrating (4), primarily (4), touch (4), cones (4), ellipsoids (4), elliptic (4), paraboloids (4), lie (4), symmetric (4), dimensions (4), prep (4), cosines (4), mathematical (4), end (4), representation (4), cannot (4), unpleasant (4), convergent (4), flexible (4), following (4), yield (4), conclusive (4), relate (4), ways (4), focus (4), like (4), origin (4), person (4), life (4), span (4), light (4), submerged (4), integrands (4), away (4), quotients (4), subtleties (4), defining (4), easily (4), rotation (4), volumes (4), cost (4), revenue (4), uses (4), until (4), indeterminate (4), shape (4), local (4), global (4), sketching (4), unable (4), log (4), calculators (4), range (4), selected (4), surviving (4), inconsistent (4), careful (4), consider (4), intercepts (4), hyperbola (4), ellipse (4), parabola (4), divide (4), combining (4), appear (4), radical (4), mistakes (4), sudden (4), misconceptions (4), error (4), misconception (4), faq (3), privacy (3), contact (3), best (3), mathematics (3), portion (3), interest (3), was (3), directly (3), reading (3), people (3), say (3), itself (3), seem (3), comments (3), list (3), commonly (3), regularly (3), sheet (3), except (3), shrunk (3), good (3), grasp (3), iterated (3), magnitude (3), centroid (3), heavily (3), inflection (3), concavity (3), decent (3), reflections (3), reducible (3), had (3), download (3), enough (3), though (3), broken (3), smaller (3), steps (3), accessible (3), regardless (3), teach (3), extra (3), spend (3), theorems (3), covering (3), finish (3), multiplying (3), homework (3), 2026 (2), tried (2), document (2), conjugate (2), modulus (2), 2320 (2), 2415 (2), 2414 (2), 2413 (2), 1314 (2), listing (2), made (2), downloadable (2), access (2), lamar (2), sources (2), disk (2), contrast (2), boundaries (2), generates (2), circular (2), ring (2), farther (2), operator (2), laplacian (2), smooth (2), expect (2), represents (2), odd (2), happen (2), familiar (2), makes (2), size (2), small (2), twice (2), deal (2), possibility (2), difficulty (2), updated (2), 2nd (2), issues (2), illustrates (2), who (2), illustrated (2), index (2), interconnected (2), tanks (2), predator (2), prey (2), populations (2), account (2), vibration (2), masses (2), wall (2), nth (2), deriving (2), centers (2), spirals (2), stability (2), constructed (2), text (2), once (2), determinant (2), traditional (2), restrict (2), ourselves (2), purposes (2), larger (2), rise (2), forcing (2), reason (2), becomes (2), apparent (2), bit (2), advantage (2), tends (2), check (2), opposite (2), avoids (2), wouldn (2), otherwise (2), damper (2), external (2), forces (2), act (2), examination (2), making (2), guess (2), complimentary (2), pair (2), fundamentals (2), autonomous (2), classifying (2), asymptotically (2), unstable (2), semi (2), substance (2), dissolved (2), enters (2), exits (2), enter (2), exit (2), influence (2), gravity (2), air (2), resistance (2), existence (2), uniqueness (2), pick (2), explanation (2), encountered (2), typical (2), oriented (2), inside (2), computed (2), parameterizing (2), skill (2), understood (2), ago (2), converted (2), generalize (2), conversion (2), portions (2), rectangles (2), interpreted (2), net (2), fubini (2), rectangle (2), giving (2), justification (2), why (2), allowed (2), goes (2), closed (2), valid (2), earlier (2), significant (2), holding (2), fastest (2), variants (2), depending (2), turn (2), writing (2), longer (2), clairaut (2), directions (2), issue (2), keep (2), mind (2), exist (2), projections (2), multiplication (2), expand (2), evaluated (2), maclaurin (2), expense (2), specific (2), impossible (2), represented (2), met (2), conditionally (2), sign (2), provided (2), telescoping (2), harmonic (2), sums (2), manipulate (2), examining (2), hence (2), monotonic (2), above (2), developed (2), enclosed (2), shaped (2), vaguely (2), pie (2), pizza (2), outer (2), pole (2), eliminate (2), waits (2), checkout (2), counter (2), bulb (2), none (2), depend (2), factors (2), wait (2), blub (2), plates (2), result (2), anyway (2), discontinuous (2), mix (2), rewrite (2), simplify (2), sines (2), secants (2), modify (2), technique (2), likely (2), road (2), constants (2), confusion (2), talk (2), affect (2), scenes (2), speak (2), feel (2), fuller (2), upper (2), rules (2), found (2), treating (2), dealt (2), revolutions (2), easy (2), shells (2), applies (2), requirements (2), shows (2), close (2), motivation (2), lies (2), integrate (2), cursory (2), profit (2), everything (2), thing (2), reasons (2), want (2), previously (2), depends (2), constraint (2), satisfy (2), squares (2), boxes (2), rolle (2), changes (2), classify (2), largest (2), smallest (2), extreme (2), fermat (2), computational (2), aid (2), sometimes (2), easier (2), importantly (2), allows (2), quantity (2), explicitly (2), knowing (2), hand (2), relationships (2), tan (2), relates (2), gets (2), large (2), sense (2), looks (2), squeeze (2), conceptual (2), meaning (2), manipulations (2), trickier (2), messy (2), due (2), memorized (2), triangle (2), gauss (2), jordan (2), compound (2), growth (2), decay (2), earthquake (2), intensity (2), takes (2), sciences (2), running (2), fraction (2), decomposition (2), asking (2), rough (2), leading (2), increase (2), decrease (2), bound (2), multiplicity (2), remainder (2), divisor (2), synthetic (2), algorithm (2), complicated (2), cubic (2), miscellaneous (2), vertex (2), acknowledge (2), talked (2), verify (2), relations (2), intercept (2), parallel (2), perpendicular (2), ordered (2), pairs (2), quadrants (2), discussing (2), introducing (2), less (2), inequality (2), proceed (2), proper (2), turned (2), procedure (2), discriminant (2), specifically (2), property (2), pricing (2), overlook (2), ability (2), lowest (2), greatest (2), grouping (2), simplified (2), rationalize (2), denominator (2), essential (2), mathjax (2), links (2), misc (2), search (2), exam (2), exams (2), guide (2), expected (2), operations (2), incorrect (2), correct (2), watch (2), simplifying (2), refresher (2), remind (2), select (2), worked (2), examined (2), jump, modified, sunday, july, 2003, dawkins, statement, short, advice, haven, ignore, five, addresses, provide, purpose, beyond, college, picture, nor, whole, containing, importance, trouble, permits, geared, towards, occasional, reviews, long, entries, somewhat, reminders, comes, prints, completely, filled, includes, assumes, reader, projection, rely, hospitals, exposure, extensively, plot, subjects, descriptions, pdf, format, navigate, menu, instructors, slowly, years, duties, department, future, felt, appropriate, click, link, present, gotten, wanting, prerequisite, assumptions, description, welcome, free, along, hope, university, edu, via, google, hide, current, studying, rationalizing, reference, summaries, options, traditionally, multi, stoke, reinforce, advanced, applicable, book, introductory, domains, ranges, finally, downloads, skip, content,

Text of the page (random words):
these equations will have multiple variables in them and we will be asked to solve the equation for one of the variables this is something that we will be asked to do on a fairly regular basis quadratic equations part i in this section we will start looking at solving quadratic equations specifically we will look at factoring and the square root property in this section quadratic equations part ii in this section we will continue solving quadratic equations we will use completing the square to solve quadratic equations in this section and use that to derive the quadratic formula the quadratic formula is a quick way that will allow us to quickly solve any quadratic equation quadratic equations a summary in this section we will summarize the topics from the last two sections we will give a procedure for determining which method to use in solving quadratic equations and we will define the discriminant which will allow us to quickly determine what kind of solutions we will get from solving a quadratic equation applications of quadratic equations in this section we will revisit some of the applications we saw in the linear application section only this time they will involve solving a quadratic equation included are examples in distance rate problems and work rate problems equations reducible to quadratic in form not all equations are in what we generally consider quadratic equations however some equations with a proper substitution can be turned into a quadratic equation these types of equations are called quadratic in form in this section we will solve this type of equation equations with radicals in this section we will discuss how to solve equations with square roots in them as we will see we will need to be very careful with the potential solutions we get as the process used in solving these equations can lead to values that are not in fact solutions to the equation linear inequalities in this section we will start solving inequalities we will concentrate on solving linear inequalities in this section both single and double inequalities we will also introduce interval notation polynomial inequalities in this section we will continue solving inequalities however in this section we move away from linear inequalities and move on to solving inequalities that involve polynomials of degree at least 2 rational inequalities we continue solving inequalities in this section we now will solve inequalities that involve rational expressions although as we ll see the process here is pretty much identical to the process used when solving inequalities with polynomials absolute value equations in this section we will give a geometric as well as a mathematical definition of absolute value we will then proceed to solve equations that involve an absolute value we will also work an example that involved two absolute values absolute value inequalities in this final section of the solving chapter we will solve inequalities that involve absolute value as we will see the process for solving inequalities with a lt i e a less than is very different from solving an inequality with a gt i e greater than graphing and functions in this chapter we ll look at two very important topics in an algebra class first we will start discussing graphing equations by introducing the cartesian or rectangular coordinates system and illustrating use of the coordinate system to graph lines and circles we will also formally define a function and discuss graph functions and combining functions we will also discuss inverse functions graphing in this section we will introduce the cartesian or rectangular coordinate system we will define introduce ordered pairs coordinates quadrants and x and y intercepts we will illustrate these concepts with a couple of quick examples lines in this section we will discuss graphing lines we will introduce the concept of slope and discuss how to find it from two points on the line in addition we will introduce the standard form of the line as well as the point slope form and slope intercept form of the line we will finish off the section with a discussion on parallel and perpendicular lines circles in this section we discuss graphing circles we introduce the standard form of the circle and show how to use completing the square to put an equation of a circle into standard form the definition of a function in this section we will formally define relations and functions we also give a working definition of a function to help understand just what a function is we introduce function notation and work several examples illustrating how it works we also define the domain and range of a function in addition we introduce piecewise functions in this section graphing functions in this section we discuss graphing functions including several examples of graphing piecewise functions combining functions in this section we will discuss how to add subtract multiply and divide functions in addition we introduce the concept of function composition inverse functions in this section we define one to one and inverse functions we also discuss a process we can use to find an inverse function and verify that the function we get from this process is in fact an inverse function common graphs in this chapter we will look at graphing some of the more common functions you might be asked to graph we graph parabolas ellipses hyperbolas and rational functions in this chapter we will also look at transformations of functions and introduce the concept of symmetry lines circles and piecewise functions this section is here only to acknowledge that we ve already talked about graphing these in a previous chapter parabolas in this section we will be graphing parabolas we introduce the vertex and axis of symmetry for a parabola and give a process for graphing parabolas we also illustrate how to use completing the square to put the parabola into the form f x a x h 2 k ellipses in this section we will graph ellipses we introduce the standard form of an ellipse and how to use it to quickly graph an ellipse hyperbolas in this section we will graph hyperbolas we introduce the standard form of a hyperbola and how to use it to quickly graph a hyperbola miscellaneous functions in this section we will graph a couple of common functions that don t really take all that much work to do but will be needed in later sections we ll be looking at the constant function square root absolute value and a simple cubic function transformations in this section we will be looking at vertical and horizontal shifts of graphs as well as reflections of graphs about the x and y axis collectively these are often called transformations and if we understand them they can often be used to allow us to quickly graph some fairly complicated functions symmetry in this section we introduce the idea of symmetry we discuss symmetry about the x axis y axis and the origin and we give methods for determining what if any symmetry a graph will have without having to actually graph the function rational functions in this section we will discuss a process for graphing rational functions we will also introduce the ideas of vertical and horizontal asymptotes as well as how to determine if the graph of a rational function will have them polynomial functions in this chapter we will take a more detailed look at polynomial functions we will discuss dividing polynomials finding zeroes of polynomials and sketching the graph of polynomials we will also look at partial fractions even though this doesn t really involve polynomial functions dividing polynomials in this section we ll review some of the basics of dividing polynomials we will define the remainder and divisor used in the division process and introduce the idea of synthetic division we will also give the division algorithm zeroes roots of polynomials in this section we ll define the zero or root of a polynomial and whether or not it is a simple root or has multiplicity k we will also give the fundamental theorem of algebra and the factor theorem as well as a couple of other useful facts graphing polynomials in this section we will give a process that will allow us to get a rough sketch of the graph of some polynomials we discuss how to determine the behavior of the graph at x intercepts and the leading coefficient test to determine the behavior of the graph as we allow x to increase and decrease without bound finding zeroes of polynomials as we saw in the previous section in order to sketch the graph of a polynomial we need to know what it s zeroes are however if we are not able to factor the polynomial we are unable to do that process so in this section we ll look at a process using the rational root theorem that will allow us to find some of the zeroes of a polynomial and in special cases all of the zeroes partial fractions in this section we will take a look at the process of partial fractions and finding the partial fraction decomposition of a rational expression what we will be asking here is what smaller rational expressions did we add and or subtract to get the given rational expression this is a process that has a lot of uses in some later math classes it can show up in calculus and differential equations for example exponential and logarithm functions in this chapter we will introduce two very important functions in many areas the exponential and logarithm functions we will look at their basic properties applications and solving equations involving the two functions if you are in a field that takes you into the sciences or engineering then you will be running into both of these functions exponential functions in this section we will introduce exponential functions we will give some of the basic properties and graphs of exponential functions we will also discuss what many people consider to be the exponential function f x bf e x logarithm functions in this section we will introduce logarithm functions we give the basic properties and graphs of logarithm functions in addition we discuss how to evaluate some basic logarithms including the use of the change of base formula we will also discuss the common logarithm log x and the natural logarithm ln x solving exponential equations in this section we will discuss a couple of methods for solving equations that contain exponentials solving logarithm equations in this section we will discuss a couple of methods for solving equations that contain logarithms also as we ll see with one of the methods we will need to be careful of the results of the method as it is always possible that the method gives values that are in fact not solutions to the equation applications in this section we will look at a couple of applications of exponential functions and an application of logarithms we look at compound interest exponential growth and decay and earthquake intensity systems of equations in this chapter we will take a look at solving systems of equations we will solve linear as well as nonlinear systems of equations we will also take a quick look at using augmented matrices to solve linear systems of equations linear systems with two variables in this section we will solve systems of two equations and two variables we will use the method of substitution and method of elimination to solve the systems in this section we will also introduce the concepts of inconsistent systems of equations and dependent systems of equations linear systems with three variables in this section we will work a couple of quick examples illustrating how to use the method of substitution and method of elimination introduced in the previous section as they apply to systems of three equations augmented matrices in this section we will look at another method for solving systems we will introduce the concept of an augmented matrix this will allow us to use the method of gauss jordan elimination to solve systems of equations we will use the method with systems of two equations and systems of three equations more on the augmented matrix in this section we will revisit the cases of inconsistent and dependent solutions to systems and how to identify them using the augmented matrix method nonlinear systems in this section we will take a quick look at solving nonlinear systems of equations a nonlinear system of equations is a system in which at least one of the equations is not linear i e has degree of two or more note as well that the discussion here does not cover all the possible solution methods for nonlinear systems solving nonlinear systems is often a much more involved process than solving linear systems review in this chapter we give a brief review of selected topics from algebra and trig that are vital to surviving a calculus course included are functions trig functions solving trig equations and equations exponential logarithm functions and solving exponential logarithm equations functions in this section we will cover function notation evaluation determining the domain and range of a function and function composition inverse functions in this section we will define an inverse function and the notation used for inverse functions we will also discuss the process for finding an inverse function trig functions in this section we will give a quick review of trig functions we will cover the basic notation relationship between the trig functions the right triangle definition of the trig functions we will also cover evaluation of trig functions as well as the unit circle one of the most important ideas from a trig class and how it can be used to evaluate trig functions solving trig equations in this section we will discuss how to solve trig equations the answers to the equations in this section will all be one of the standard angles that most students have memorized after a trig class however the process used here can be used for any answer regardless of it being one of the standard angles or not trig equations with calculators part i in this section we will discuss solving trig equations when the answer will generally require the use of a calculator i e they aren t one of the standard angles note however the process used here is identical to that for when the answer is one of the standard angles the only difference is that the answers in here can be a little messy due to the need of a calculator included is a brief discussion of inverse trig functions trig equations with calculators part ii in this section we will continue our discussion of solving trig equations when a calculator is needed to get the answer the equations in this section tend to be a little trickier than the normal trig equation and are not always covered in a trig class exponential functions in this section we will discuss exponential functions we will cover the basic definition of an exponential function the natural exponential function i e bf e x as well as the properties and graphs of exponential functions logarithm functions in this section we will discuss logarithm functions evaluation ...