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MATH 153 Syllabus

Calculus I

Revised: September 2022

Course Description

Limits, continuity, derivative, and integrals of algebraic and trigonometric functions with applications.
Prerequisite: MATH 146 or placement
Four semester hours

Student Learning Objectives

By the end of the course, the student will be able to:

  • Use limit rules to calculate various limits
  • Calculate the derivative of several basic functions using the definition
  • Understand the geometrical meaning of the derivative of a function
  • Solve acceleration/velocity/position problems
  • Use derivative rules to differentiate functions
  • Calculate derivatives of functions defined implicitly
  • Determine relative and absolute maximum and minimum values of a function
  • Calculate higher derivatives and use them to determine intervals where a function is increasing/decreasing and concave-up/concave-down
  • Solve optimization problems
  • Determine simple antiderivatives using the basic rules of differentiation
  • Evaluate Riemann sums in order to evaluate definite integrals
  • Describe and apply the Fundamental Theorem of Calculus
  • Evaluate definite integrals to find areas under and between curves

Text

Online Text: Herman and Strang. Calculus Volume 1, OpenStax, 2016.

Text Book Link: https://openstax.org/details/books/calculus-volume-1

Grading Procedure

Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.

Attendance Policy

Attendance policy is left to the discretion of individual instructors, subject to general university policy.

Course Outline:

  1. CHAPTER 1 – Functions and Graphs (.5 week)
    Selected precalculus topics/summary of chapter (approximately a week) chosen at the instructor's discretion.
    • Section 1: Review of Functions (optional)
    • Section 2: Basic Classes of Functions (optional)
    • Section 3: Trigonometric Functions (optional)
    • Section 4: Inverse Functions (optional)
    • Section 5: Exponential and Logarithmic Functions (optional)
  2.  CHAPTER 2 — Limits (3 weeks)
    • Section 1: A Preview of Calculus
    • Section 2: The Limit of a Function
    • Section 3: The Limit Laws
    • Section 4: Continuity
    • Section 5: The Precise Definition of a Limit (optional)
  3. CHAPTER 3 — Derivatives (4.5 weeks)
    • Section 1: Defining the Derivative
    • Section 2: The Derivative as a Function
    • Section 3: Differentiation Rules (this includes product rule and quotient rule)
    • Section 4: Derivatives as Rates of Change
    • Section 5: Derivatives of Trigonometric Functions
    • Section 6: The Chain Rule
    • Section 7: Derivatives of Inverse Functions (optional)
    • Section 8: Implicit Differentiation (including the derivatives of inverse trigonometric functions)
    • Section 9: Derivatives of Exponential and Logarithmic Functions
  4. CHAPTER 4 — Applications of Derivatives (3 weeks)
    • Section 1: Related Rates
    • Section 2: Linear Approximations and Differentials
    • Section 3: Maxima and Minima
    • Section 4: The Mean Value Theorem
    • Section 5: Derivatives and the Shape of a Graph
    • Section 6: Limits at Infinity and Asymptotes
    • Section 7: Applied Optimization Problems
    • Section 8: L'Hopital's rule
    • Section 9: Newton’s Method (optional)
    • Section 10: Antiderivatives.
  5.  CHAPTER 5 —Integrals (2.5 weeks)
    • Section 1: Approximating Areas
    • Section 2: The Definite Integral
    • Section 3: The Fundamental Theorem of Calculus
    • Section 4: Integration Formulas and the Net Change Theorem (the Net Change Theorem is optional)
    • Section 5: Substitution
    • Section 6: Integrals Involving Exponential and Logarithmic Functions (optional)
    • Section 7: Integrals Resulting in Inverse Trigonometric Functions (optional) 
  6.  CHAPTER 6 — Applications of Integration (.5 week)
    • Section 1: Areas between curves (optional)

 

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