# 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.

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

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)