MATH 2417 CALCULUS SYLLABUS
 (Larson/Hostetler/Edwards) 8th Edition

P.1 Graphs and Models
P.2 Linear Models and Rates of Change
P.3 Functions and their Graphs
P.4 Fitting Models to Data

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

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 Relates Rates

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
3.4 Concavity and the second Derivative Test
3.5 Limits at Infinity
3.6 A summary of Curve Sketching
3.7 Optimization Problems
3.9 Differentials

4. Integration

4.1 Antiderivatives and Indefinite Integration
4.2 Area
4.3 Riemann Sums and the Definite Integral
4.4 The Fundamental Theorem of Calculus
4.5 Integration by Substitution

5. Logarithmic, Exponential, and Other Transcendental Functions

5.1 The Natural Logarithmic Function and Differentiation
5.2 The Natural Logarithmic Function and Integration
5.3 Inverse Functions
5.4 Exponential Functions: Differentiation and integration
5.5 Bases other than e and Applications
5.6 Inverse Trigonometric Functions and Differentiation
5.7 Inverse Trigonometric Functions: Integration and Completing the Square

7. Applications of Integration

7.1 Area of a Region Between Two Curves
7.2 Volume: The Disc Method
7.3 Volume: The Shell Method
7.4 Arc Length and Surfaces of Revolution

8. Integration Techniques, L'Hôpital's Rule, and Improper Integrals

8.1 Basic Integration Rules
8.2 Integration by Parts
8.3 Trigonometric Integrals
8.4 Trigonometric Substitution
8.5 Partial Fractions
8.7 Indeterminate Forms and L'Hôspital's Rule  
 

Appendix B Proofs of Selected Theorems

Appendix C   Integration Tables