MATH 2515: Calculus & Analytic Geometry I

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Subject:
Mathematics
Credit hours: 5 Lecture hours: 5 Lab hours: 0
PCS code (Local ID):
Baccalaureate/Transfer
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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.

Prerequisite(s)

Grades of C or better in both MATH 1803 and MATH 1814 or appropriate assessment score

Prerequisite(s) or Corequisite(s)

Appropriate assessment score or completion/concurrent enrollment in ENGL 1422 with a grade of C or better

IAI Number
M1 900-1
MTH 901
IAI Title
Calculus I
Calculus I
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
  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
  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

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.