Course Description
Derivatives and integrals are carefully developed as applications of the limit concept. These ideas are extended to algebraic, trigonometric, and logarithmic functions. A strong emphasis is given to applications in physics, geometry, and other sciences. IAI: MTH 901 Mathematics. IAI: M1 900-1.
Prerequisite(s)
Grades of C or better in both MATH 1803 and MATH 1814 or appropriate assessment score - Must be completed prior to taking this course. Appropriate assessment score or ENGL 1422 with a grade of C or better - Must be taken either prior to or at the same time as this course.
At the end of this course, students will be able to:
- Solve limit problems using a wide variety of techniques.
- Evaluate derivatives using power, product, quotient, chain rules, and implicit differentiation.
- Find critical and inflections points and be able to graph polynomial and rational functions.
- Evaluate indefinite integrals using basic rules and integration by substitution.
- Calculate areas with definite integrals.
- Find derivatives and integrals of transcendental functions.
- Use derivatives and integrals in applications involving, but not limited to, rates of change, optimization, volumes, and centers of mass.
Topical Outline
1. Review of Functions
2. Representing Functions
3. Inverse, Exponential, and Logarithmic Functions
4. Trigonometric Functions and Their Inverses
5. The Idea of Limits
6. Definitions of Limits
7. Techniques for Computing Limits
8. Infinite Limits
9. Limits at Infinity
2. Representing Functions
3. Inverse, Exponential, and Logarithmic Functions
4. Trigonometric Functions and Their Inverses
5. The Idea of Limits
6. Definitions of Limits
7. Techniques for Computing Limits
8. Infinite Limits
9. Limits at Infinity
10. Continuity
11. Introducing the Derivative
12. Working with Derivatives
13. Rules of Differentiation
14. The Product and Quotient Rules
15. Derivatives of Trigonometric Functions
16. Derivatives as Rates of Change
17. The Chain Rule
18. Implicit Differentiation
19. Derivatives of Logarithmic and Exponential Functions
20. Derivatives of Inverse Trigonometric Functions
21. Related Rates
22. Maxima and Minima
23. What Derivatives Tell Us
11. Introducing the Derivative
12. Working with Derivatives
13. Rules of Differentiation
14. The Product and Quotient Rules
15. Derivatives of Trigonometric Functions
16. Derivatives as Rates of Change
17. The Chain Rule
18. Implicit Differentiation
19. Derivatives of Logarithmic and Exponential Functions
20. Derivatives of Inverse Trigonometric Functions
21. Related Rates
22. Maxima and Minima
23. What Derivatives Tell Us
24. Graphing Functions
25. Optimization Problems
26. Linear Approximations and Differentials
27. Mean Value Theorem
28. Antiderivatives
29. Approximating Areas under Curves
30. Definite Integrals
31. Fundamental Theorem of Calculus
32. Working with Integrals
33. Substitution Rule
34. Velocity and Net Change
35. Regions Between Curves
36. Volume by Slicing
37. Volume by Shells
38. Length of Curves
39. Physical Applications
27. Mean Value Theorem
28. Antiderivatives
29. Approximating Areas under Curves
30. Definite Integrals
31. Fundamental Theorem of Calculus
32. Working with Integrals
33. Substitution Rule
34. Velocity and Net Change
35. Regions Between Curves
36. Volume by Slicing
37. Volume by Shells
38. Length of Curves
39. Physical Applications