math 241: Calculus and Analytic Geometry I (4)


Course Prerequisites/Corequisites: MATH 241.

Course Description:Inequalities, functions, graphs, straight lines, linear equations, limits, continuity, differentiation, maximum-minimum problems, mean value theorem, related rates, and indefinite integrals. Four hours of lecture per week.
Listed as MATH 2413 in the Texas Common Course Numbering System.

Required Reading / Textbook: Calculus: Early Transcendentals. Sullivan and Miranda, W.H. Freemand and Company

Major Assignments/Exams

  • Homework
  • Quizzes
  • Exams
  • Final Exam

Course topics

CHPATER 2. Limits

  • 2.1 The Idea of Limits
  • 2.2 Definitions of Limits
  • 2.3 Techniques for Computing Limits
  • 2.4 Infinite Limits
  • 2.5 Limits at Infinity
  • 2.6 Continuity
  • 2.7 Precise Definitions of Limits (optional)

CHPATER 3. Derivatives.

  • 3.1 Introducing the Derivative
  • 3.2 Rules of Differentiation
  • 3.3 The Product and Quotient Rules
  • 3.4 Derivatives of Trigonometric Functions
  • 3.5 Derivatives as Rates of Change
  • 3.6 The Chain Rule
  • 3.7 Implicit Differentiation
  • 3.8 Derivatives of Logarithmic and Exponential Functions
  • 3.9 Derivatives of Inverse Trigonometric Functions
  • 3.10 Related Rates

CHPATER 4. Applications of the Derivative

  • 4.1 Maxima and Minima
  • 4.2 What Derivatives Tell Us
  • 4.3 Graphing Functions
  • 4.4 Optimization Problems
  • 4.5 Linear Approximation and Differentials
  • 4.6 Mean Value Theorem
  • 4.7 L’Hôpital’s Rule
  • 4.8 Antiderivatives

CHPATER 5. Integration

  • 5.3 Fundamental Theorem of Calculus (if time permits)
  • 5.4 Working with Integrals (if time permits)
  • 5.5 Substitution Rule(if time permits)

CHPATER6. Applications of Integration

  • 6.2 Regions between Curves (if time permits)

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