Definition, domain range, Graphs of functions, Representing a function numerically, the vertical line test for a function, Piecewise defined functions, Increasing and decreasing functions, Even and odd function, Common functions: linear, power, polynomial, rational functions

All worked out examples of 1.1. Exercises 1.1: 1-8, 15, 18, 23, 25, 26

Combining functions:Shifting and Scaling graphs Sums, differences, products and quotients, Composite functions, Shifting a graph of a function

Worked out examples: 1-5 Exercises 1.2: 1-8

Graphing with calculator and computers (desmos may be easy) to plot the graph of the functions (some of the functions)

y = x, y = x2, y = 1/(1 −x), y = sin x, y = cos x, y = sin 100x

Exponential functions: Definition, Exponential behavior, Exponential growth and decay

Worked out examples: 1-4 Exercises 1.5: 29-33

Inverse Functions and Logarithms Worked out examples: 1 - 4, 6, 7

Exercises 1.5: 79 - 81

Rate of change and tangent to curves. Worked out examples: 1-5

Exercises 2.1: 1, 3, 6, 7, 9, 15, 17

Limit of a Function and Limit Laws Limits of function values, The limit laws, Eliminating zero denominators algebraically, The Sandwich theorem(no proof)

Worked out examples: 1-11

The Precise Definition of a Limit: Definition of limit

Worked out examples: 1-5

One sided limit: Worked out Examples 1-4

Continuity

Worked out examples: 2, 3

Intermediate Value Theorem for Continuous Functions

Worked out examples: 11, 12

Limits Involving Infinity; Asymptotes of Graphs

Worked out examples 1, 2, 3

Horizontal Asymptotes

Worked out examples: 4-9

Oblique asymptotes

Worked out examples: 10-14

Vertical asymptotes

Worked out examples: 15-19

Some related problems

Tangents and the Derivative at a Point Finding a Tangent to the Graph of a Function Rates of Change: Derivative at a point

Worked out Examples: 1, 2 Exercises 3.1: 5-8, 11, 12, 13, 23, 24, 25

The Derivative as a function

Worked out Examples: 4, 5

Differentiable Functions are continuous

The Derivative as a rate of change Worked out Examples: 1-7 Ideas of derivatives of trigonometric, inverse trigonometric, logarithm, exponential functions and ideas of chain rules

Related rates

Worked out Examples: 1-6

Extreme values of functions: Introduction

Worked out examples: 1-4 Exercise 4.1: 21, 22, 23, 31, 32

The mean value theorem Rolle’s Theorem(no proof), Lagrange mean value theorem(no proof)

Worked out examples: 1-4

Monotonic functions and the first derivative test Increasing functions and decreasing Functions

Worked out examples: 1, 2, 3

Concavity and curve sketching

Worked out examples: 1-9

Indeterminate Forms and LHpitals Rule Indeterminate form, LHpitals rule

All worked out examples Exercises 4.5: 1-7, 13, 15

Applied optimization

Worked out examples: 1-5

Newton’s method

Worked out examples: 1, 2 Examples 4.7: 1-4

Antiderivatives

Worked out examples: 1, 2, 3

Area and Estimating with Finite Sums Area

worked out examples: 1-4 Exercises 5.1: 1-4

Sigma notation and limits of finite sums

Worked out examples: 1-5

The definite integral

Worked out example: 4, 5

The fundamental theorem of calculus

Mean value theorem for definite integrals, Fundamental theorem of calculus Part 1 and 2 (no proof), The net change theorem

Worked out examples: 2-7

Indefinite integral and substitution method

All worked out examples

Area between the curves

Worked out examples: 4, 5, 6, 7 Exercises 5.6 : 63-66

Volumes using cylindrical shells

Worked out examples: 1-10

Volumes using cross-sections

Worked out examples: 2, 3

Arc length

Worked out examples: 1, 2 3, 4, 5

Areas of surfaces of revolution

Worked out examples: 1, 2

Review of integration by parts, trigonometric substitutions, integration of rational functions by partial fractions. Computer algebra system (Maple)

Numerical Integration Simpsons Rule: Approximations Using Parabolas Error Analysis

Worked out examples:1-6 Exercises 8.6: 1, 2, 3, 4, 7, 8, 9, 10. 11, 12, 13, 17, 19, 21

Improper integrals

Worked out examples: 1-9

Solutions, Slope Fields, and Eulers Method General first order differential equations and solutions

Worked out examples: 1, 2

Slope Fields: Viewing Solution Curves Eulers Method

Worked out examples: 3, 4 Exercises 9.1: 11, 12, 13

First order linear equation

Worked out examples 1, 2, 3 Exercises 9.2: 1-10, 15-21

Applications... Motion with resistance proportional to velocity

Exponential change

Worked out Examples: 1, 2, 3, 4, 5

Graphical solutions of autonomous equations

Example worked out: 1

Sequences

Exercises 10.1: 1,2,3,7,8.13,16,27-32, Infinite series Worked out examples: 1-10, Related problems from exercise 10.2

Ideas of Integral test, comparison test: worked out examples, Alternating series, absolute and conditional convergence, with at least one worked out examples

Power series

Worked out examples 1-6

Taylor and Maclaurin series

Exercises 10.8: 1, 2 ,3, 4, 7, 9, 11, 12

Functions of several variables

Worked out examples: 1, 2, 3, 4

Limits and continuity in higher dimensions

Worked out Examples: 1-6, Exercises: 1, 2, 3, 4, 5, 6, 13, 14

Partial derivatives

Worked out examples: 1-10, Examples 14.3: 1-18

Chain rule

Worked out examples: 1-6

Directional derivative

Worked out examples: 1-5

Tangent planes and differentials

Worked out examples: 1-4

Extreme values and saddle points

Worked out examples: 1-5 Exercises 14.7: 1-7