Just-In-Time Algebra and Trigonometry for Early Transcendentals Calculus

Calculus SubjectsAlgebra Background

                                  (What you’ll take)                      (What you’ll need)

 

                                                           Chapter

 

                                  Review of Basics     1.    Numbers and Their Disguises

                                                                        Multiplying and dividing fractions, adding and subtracting fractions, parentheses, exponents, roots, percent, scientific notation, calculators, rounding, intervals

 

                                     Circles, Parabolas, etc.     2.    Completing the Square

                                                                        Completing the square in one and two variables

 

                                            Equations     3.    Solving Equations

                                                                                                Equations of degree 1 and 2, solving other types of equations, rational equations, the zero-factor property

 

                 AlgebraicFunctions and Graphs     4.    Functions and Their Graphs

                                                                                                Introduction, equations of lines, power functions, shifting graphs, intersection of curves

 

                              Transcendental Functions     5.    Cyclic Phenomena: The Six Basic Trigonometric Functions

                                                                              Angles, definitions of the six trigonometric functions, basic identities, special angles, sum formulas

 

                                                                                       6.    Exponential Functions

                                                                              The family of exponentials, the function

 

                                                                 7.    Composition and Inverse Functions

                                                                                                        Composite functions, the idea of inverses, finding an inverse of f given by a graph, finding the inverse of f given by an expression

 

                                                                                       8.    Logarithmic Functions

                                                                              Definition of logarithms, logs as inverses of exponential functions, laws of logarithms, the natural logarithm

 

                                                                                       9.    Inverse Trigonometric Functions

                                                                              The definition of arcsin x, the functions arctan x and arcsec x, inverse trigonometric   identities

 

                                                 Limits   10.   Changing the Form of a Function

                                                                                                Factoring, canceling, long division, rationalizing, extracting a factor from under a root

 

                                           Derivatives   11.   Simplifying Algebraic Expressions

                                                                        Working with difference quotients and rational functions, canceling common factors, rationalizing expressions

 

                                     The Chain Rule   12.   Decomposition of Functions

                                                                                                Inner, outer, and outermost functions, decomposing composite functions

 

                               Implicit Differentiation   13.   Equations of Degree 1 Revisited

                                                                        Solving linear equations involving derivatives

 

                                      Related Rates,   14.   Word Problems, Algebraic and Transcendental

                        Applied Max-Min Problems                Algebraic word problems, the geometry of rectangles, circles and spheres, trigonometric word problems, right angle triangles, the law of sines and the law of cosines, exponential growth and decay

 

              Integrating Trigonometric Functions   15.   Trigonometric Identities

                                                                            Rewriting trigonometric expressions using identities.

Appendices

A.    The Binomial Theorem

B.    Derivation of The Quadratic Formula

Answers to Exercises

Index