MAC 1311 - Course Outline
Chapter P: Preparation for Calculus
P.1 Graphs and Models
P.2 Linear Models and Rates of Change
P.3 Functions and Their Graphs - tutorial on lines, quadratics, absolute value and polynomial graphs: http://www.purplemath.com/modules/graphing.htm
quiz on piece-wise functions:
http://www.purplemath.com/moes/pcwiseq.htm
P.4 Fitting Models to Data
Review of Inverse Trigonometric Functions
Test 1
CHAPTER 1 - LIMITS AND THEIR PROPERTIES
1.1 A Preview of Calculus*
1.2 Finding Limits Graphically and Numerically*
1.3 Evaluating Limits Analytically *
1.4 Continuity and One-Sided Limits *
1.5 Infinite Limits *
CHAPTER 2 - DIFFERENTIATION
2.1 The Derivative and the Tangent Line Problem
2.2 Basic Differentiation Rules and Rates of Change*
2.3 The Product and Quotient Rules and Higher-Order Derivatives*
2.4 The Chain Rule*
2.5 Implicit Differentiation*
2.6 Related Rates
Answers for the Review Exercises Test 3
CHAPTER 3 - APPLICATIONS OF DIFFERENTIATION
3.1 Extrema on an Interval*
3.2 Rolle's Theorem and the Mean Value Theorem
3.3 Increasing and Decreasing Functions and the First
Derivative Test *
http://www.cut-the-knot.org/Curriculum/Calculus/CubicSpline.shtml
3.4 Second Derivative Test and Concavity *
3.5 Limits and Infinity
3.6 Summary of Curve Sketching *
3.7 Optimization Problems
3.8 Newton's Method
3.9 Differentials
3.10 Business and Economic Applications
Answer Key for Review Exercises 2 - Test 4
Answer Key for Review Exercises 4 - Test 4
CHAPTER 4 - INTEGRATION
4.1 Antiderivatives and Indefinite Integration*
4.2 Area
4.3 Reimann Sums and the Definite Integral
http://www.cut-the-knot.org/Curriculum/Calculus/RiemannSums.shtml
4.4 The Fundamental Theorem of Calculus*
6.1 Area of a Region Between Two Curves
4.5 Integration by Substitution*
4.6 Numerical Integration
CHAPTER 5 - LOGARITHMIC, EXPONENTIAL, AND OTHER TRANSCENDENTAL FUNCTIONS
5.1 Natural Logarithmic Function and Differentation*
5.2 Natural Logarithmic Function and Integration*
5.3 Inverse Functions*
5.4 Exponential Function*
5.5 Bases other than e and Applications*
5.6 Differential Equations: Growth and Decay
5.7 Differential Equations: Separation of Variables
5.7 Inverse Trigonometric Functions and Differentation*
5.8 Inverse Trigonometric Functions, Integration*
Practice Sheet on e's, a's and logs
Answer key for Practice Sheet on e's, a's and logs
Answer Key for Practice Test 1
Answer key for Practice Test 4 page 1 page 2
Test 6
CHAPTER 6 - APPLICATIONS OF INTEGRATION
6.1 Area of the Region Between Two Curves
6.2 Volume: The Disk Method (optional)
6.3 Volume: The Shell Method (optional)
CHAPTER 7 - INTEGRATION TECHNIQUES, L'HOSPITAL'S RULE, AND IMPROPER INTEGRALS
7.7 Indeterminate Forms and L'Hopital's Rule
7.2 Integration by Parts
Final Examination
* Videotapes are available on these topics.