MAC 2311 (sec 12829): Calculus - Analytic Geometry I

• Concept of limit, definition and calculation of limits
• Tangents, velocities, and other rates of change
• Concept of a differentiable function
• Derivatives of polynomials and exponential functions
• Computing the derivative of products and quotients
• Applications, trigonometric functions
• Chain rule for derivatives
• Implicit differentiation
• Higher derivatives, logarithmic and hyperbolic functions
• Computing minima and maxima of functions
• Mean value theorem, l'Hospital's rule
• Graphing curves
• Applications
• Concept of the integral, fundamental theorem of calculus
• Substitution rule for integrals
• Applications of differentiation and integration

• Jan 8, 2007: quick recall of some basic notions for functions; the tangent problem
  Literature: [Ste03, Ch. 1, Ch. 2.1]
• Jan 10, 2007: one- and two-sided limits, vertical asymptotes
  Literature: [Ste03, Ch. 1, Ch. 2.2]
• Jan 11, 2007: computing with limits, continuous functions
  Literature: [Ste03, Ch. 1, Ex. 23, 24, 32 of Ch. 2.2, limit laws in Ch. 2.3, Theorem 8 in Ch. 2.5]
• Jan 12, 2007: handling limits of fractions
  Literature: [Ste03, Ch. 2.3]
• Jan 17, 2007: squeezing theorem, classes of continuous functions
  Literature: [Ste03, Ch 2.3, Ch. 2.5]
• Jan 18, 2007: intermediate value theorem, horizontal asymptotes
  Literature: [Ste03, Ch 2.5, Ch. 2.6]
• Jan 19, 2007: slope of a tangent and derivative of a function
  Literature: [Ste03, Ch. 2.7, Ch. 2.8, Ch. 2.9]
• Jan 22, 2007: computing simple derivatives
  Literature: [Ste03, Ch. 3.1]
• Jan 24, 2007: an application of Calculus in geometry, computing simple derivatives
  Literature: [Ste03, Ex. 60 in Ch. 2.3, Ch. 3.1]
• Jan 25, 2007: rules for differentiation; Homework #1 is available
  Literature: [Ste03, Ch. 3.2, Ch 3.4, Ch. 3.5]
• Jan 26, 2007: proof of the chain rule
  Literature: [Ste03, Ch. 3.5]
• Jan 29, 2007: implicit differentiation
  Literature: [Ste03, Ch. 3.6]
• Jan 31, 2007: implicit differentiation
  Literature: [Str03, Ch. 3.6, Ex. 69 in Ch. 3.6]
• Feb 1, 2007: hyberbolic functions
  Literature: [Str03, Ch. 3.9]
• Feb 2, 2007: inverse hyberbolic functions, examples for computing derivatives
  Literature: [Str03, Ch. 3.9]
• Feb 5, 2007: higher derivatives, mathematical induction
  Literature: [Str03, Ch 3.7, Ch. 1 (p. 81)]
• Feb 7, 2007: maximum and minium values; Fermat's theorem
  Literature: [Str03, Ch. 4.1]
• Feb 8, 2007: Rolle's theorem
  Literature: [Str03, Ch. 4.2]
• Feb 9, 2007: applying Rolle's theorem
  Literature: [Str03, Ch. 4.2]
• Feb 12, 2007: examples reviewing the computation of limits; Homework #2 is available
  
• Feb 14, 2007: Mean Value Theorem
  Literature: [Str03, Ch. 4.2]
• Feb 15, 2007: first and second derivative test
  Litrature: [Str03, Ch. 4.3]
• Feb 16, 2007: inflection points; an example for finding the graph of a function
  Literature: [Str03, Ch. 4.3]
• Feb 19, 2007: sketching the graph of a function
  Literature: [Str03, Ch. 4.3]]
• Feb 21, 2007: l'Hospital's rule
  Literature: [Str03, Ch. 4.4]
• Feb 22, 2007: Newton's Method
  Literature: [Str03, Ch. 4.9]
• Feb 23, 2007: Newton's Method; slant asymptotes
  Literature: [Str03, Ch. 4.4, Ch. 4.9]
• Feb 26, 2007: antiderivatives
  Literature: [Str03, Ch. 4.10]
• Feb 28, 2007: the area problem
  Literature: [Str03, Ch. 5.1]
• Mar 1, 2007: geometry of antiderivatives; definition of a definite integral
  Literature: [Str03, Ch. 4.10, Ch. 5.2]
• Mar 2, 2007: Solutions for Homework #1; Exam X1 is available
• Mar 12, 2007: Fundamental Theorem of Calculus, Part 1
  Literature: [Str03, Ch. 5.3]
• Mar 14, 2007: Fundamental Theorem of Calculus, Part 2
  Literature: [Str03, Ch. 5.3]
• Mar 15, 2007: Fundamental Theorem of Calculus, Examples
  Literature: [Str03, Ch. 5.3]
• Mar 16, 2007: Fundamental Theorem of Calculus, Examples
  Literature: [Str03, Ch. 5.3, Ex. 54-56 in Ch. 5.3]
• Mar 19, 2007: substitution rule for indefinite integrals
  Literature: [Str03, Ch. 5.5]
• Mar 21, 2007: solutions to Exam X1
• Mar 22, 2007: substitution rule for indefinite integrals: examples
  Literature: [Str03, Ch. 5.5]
• Mar 23, 2007: substitution rule for definite integrals
  Literature: [Str03, Ch. 5.5]
• Mar 26, 2007: areas between curves
  Literature: [Str03, Ch. 6.1]
• Mar 28, 2007: areas between curves
  Literature: [Str03, Ch. 6.1]
• Mar 29, 2007: volumes
  Literature: [Str03, Ch. 6.2]
• Mar 30, 2007: volumes
  Literature: [Str03, Ch. 6.2]
• Apr 2, 2007: volumes by cylindrical shells
  Literature: [Str03, Ch. 6.3]
• Apr 4, 2007: volumes by cylindrical shells, average value of a function
  Literature: [Str03, Ch. 6.3, Ch. 6.5]
• Apr 5, 2007: mean value theorem for integrals, application of the intermediate value theorem
  Literature: [Str03, Ch. 6.5, Ch. 2.6 (Ex. 63)]
• Apr 6, 2007: rates of change
  Literature: [Str03, Ch. 2.6 (Ex. 54), Ch. 2.7 (Ex. 18), Ch. 2.8 (Ex. 27)]
• Apr 9, 2007: rates of change in the natural sciences; Homework #3 is available
  Literature: [Str03, Ch. 3.3 (Ex. 35, Example 1)]
• Apr 11, 2007: related rates
  Literature: [Str03, Ch. 3.10 (Example 3)]
• Apr 13, 2007: optimization problems
  Literature: [Str03, Ch. 4.7 (Example 4)]
• Apr 16, 2007: optimization problems
  Literature: [Str03, Ch. 4.7 (Example 2, Example 5)]
• Apr 18. 2007: applications of differentiation
  Literature: [Str03, Ch. 4.10 (Example 7)]
• Apr 20, 2007: applications of integration
  Literature: [Str03, Ch. 6.1 (Ex. 46)]
• Apr 23, 2007: exercises in preparation of the final exam
• Apr 25, 2007: exercises in preparation of the final exam