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This post was originally intended to be a post in the thread, Inverse Functions, a thread I started to get help learning about functions and their inverses from Guitarist and Serpicojr, but as I was typing out this post I realized that it will most likely be useful in the future, at least in reference to posts of mine, while I am learning calculus. I decided to create this post as a seperate link to make it easier to find and more accessible.
The link to the original thread is this:
http://www.thescienceforum.com/Inver...ions-8872t.php
This thread is a response to this post from Guitarist:
The book I am working from is called: Calculus Early Transcendentals 5/E Volume 1. I believe it is a text book that the sister of a coworker used to learn calculus from. The author is James Stewart.What book are you working from? It doesn't seem to me like the logical next step, unless you have already been told about series, sequences, convergence and the like. I may be wrong, but it seems to me you'll need these concepts in hand before you get into limits and derivatives.
Or maybe you were planning to start there?
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The book contains 12 chapters which are named:
1. Functions and Models
2. Limits and Derivatives
3. Differentiation Rules
4. Applications of Differentiation
5. Integrals
6. Applications of Integration
7. Techniques of Integration
8. Further Applications of Integration
9. Differential Equations
10. Parametric Equations and Polar Coordinates
11. Infinite Sequences and Series
12. Vectors and the Geometry of Space
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Chapter 1, Functions and Models, is divided into 6 sections
1.1 Four Ways to Represent a Function
1.2 Mathematical Models: A Catolog of Essential Functions
1.3 New Functinos from Old Functions
1.4 Graphing Calculators and Computers
1.5 Exponential funtions
1.6 Inverse Functions and Logarithms
Then of course about 70 review questions follow
Chapter 2, Limits and Derivatives, is divided into 9 sections
2.1 The Tangent and Velocity Problems
2.2 The Limit of a Function
2.3 Cacluating Limits of a function
2.4 Percise definition of a limit
2.5 Continuity
2.6 Limits at Infinity; Horizontal Asymptotes
2.7 Tangents, Velocities, and other rates of change
2.8 Derivities
2.9 Derivative as a function
(I might as well type in the rest of the book sections.)
Chapter 3, Differential Rules, is divided into 11 sections
3.1 Derivitives of polynomials
3.2 Product and Quotient Rules
3.3 Rates of change in the Natural and social sciences
3.4 Derivatives of trigonomentric functions
3.5 Chain rule
3.6 Implicit differentiation
3.7 Higher Derivatives
3.8 Derivatives of Logarithmic Functions
3.9 Hyperbolic functions
3.10 Related rates
3.11 Linear approximations and differentials
Chapter 4, Applications of Differentiation, is divided into 10 sections
4.1 Maximum and Minimum Values
4.2 Mean Value Theorem
4.3 How Derivatives Affect the Shape of a Graph
4.4 Indeterminate forms and L'Hospital's Rule
4.5 Summary of Curve Sketching
4.6 Graphing with calculus and calculators
4.7 Optimization Problems
4.8 Applications to business and econimics
4.9 Newton's Method
4.10 Antiderivatives
Chapter 5, Integrals, is divided into 6 sections
5.1 Areas and distances
5.2 Definte integral
5.3 Fundamental theorem of calculus
5.4 Indefinite integrasl and the net change theorem
5.5 Substitution rule
5.6 Logarithm defined as an integral
Chapter 6, Applications of Integration, is divided into 5 sections
6.1 Areas between curves
6.2 Volumes
6.3 Valumes by cylindrical shells
6.4 Work
6.5 Average value of a function
Chapter 7, Techniques of Integration, is divided into 8 sections
7.1 Integration by parts
7.2 Trigonometric Integrals
7.3 Trigonometric substitution
7.4 Integration of rational functions by partial fractions
7.5 Strategy for integratino
7.6 Integration using tables and conputer algebra systems
7.7 Approximate integration
7.8 Improper integrals
Chapter 8, Further Applications of Integration, is divided into 5 sections
8.1 Arc Length
8.2 Area of a surface of revolution
8.3 Applications to physics and engineering
8.4 Applications to economics and biology
8.5 Probablitiy
Chapter 9, Differential Equations, is divided into 7 sections
9.1 Modeling with differential equations
9.2 Direction fields and Euler's method
9.3 Separable equations
9.4 Exponential growth and decay
9.5 Logistic Equation
9.6 Linear Equations
9.7 Predator-prey systems
Chapter 10, Parametric Equations and Polar Coordinates, is divided into 6 sections
10.1 Curves defined by parametric equations
10.2 Calculus with parametric curves
10.3 Polar coordinates
10.4 Areas and lengths in polar coordinates
10.5 Conic sections
10.6 Conic sections in polar coordinates
Chapter 11, Infinite Sequences and Series, is divided into 12 sections
11.1 Sequnces
11.2 Series
11.3 Integral Test and estimates of sums
11.4 Comparison tests
11.5 Alternating series
11.6 Absolute convergence and the ratio and root tests
11.7 Strategy for testing series
11.8 Power series
11.9 Representations of functions as power series
11.10 Taylor and Maclaurin series
11.11 Binomial series
11.12 Applications of Taylor Polynomials
Chapter 12, Vectors and the Geometry of Space, is divided into 7 sections
12.1 Three-Dimentional coordinate systems (Now this I should be good at!)
12.2 Vectors
12.3 Dot product
12.4 Cross product
12.5 Equations of lines and planes
12.6 Cylinders and quadric surfaces
12.7 Cylindrical and spherical coordinates
Then the book has 8 Appendixes
A. Numbers, Inequalities, and Absolute Values
B. Coordinate Geometry and Lines
C. Graphs of Second-Degree Equations
D. Trigonometry
E. Sigma Notation
F. Proofs of Theorems
G. Complex Numbers
H. Answers to Odd-Numbered Exercises
