Syllabus: M408L

INTEGRAL CALCULUS

Text: Stewart, Calculus, Sixth Edition

Responsible Parties: Kathy Davis, John Gilbert, Diane Radin January 2008

Prerequisite and degree relevance: One of M408C, M408N, or M408K, with a grade of at least C-. Only one of the following may be counted: M403L, M408C, M408L, M408S.

Calculus is offered in two equivalent sequences: a two-semester sequence, M 408C/408D, which is recommended only for students who score at least 600 on the mathematics Level I or IC Test, and a three-semester sequence, M 408K/408L/408M.

For some degrees, the two-semester sequence M 408K/408L satisfies the calculus requirement . This sequence is also a valid prerequisite for some upper-division mathematics courses, including M325K, 427K, 340L, and 362K.

M408C and M408D (or the equivalent sequence M408K, M408L, M408M) are required for mathematics majors, and mathematics majors are required to make grades of C or better in these courses.

Course description: M408L is one of two first-year calculus courses. It is directed at students in the natural and social sciences and at engineering students. In comparison with M408D, it covers fewer chapters of the text. However, some material is covered in greater depth, and extra time is devoted the development of skills in algebra and problem solving. This is not a course in the theory of calculus.

Introduction to the theory and applications of integral calculus of functions of one variable; topics include integration, the fundamental theorem of calculus, transcendental functions, sequences, and infinite series.

Timing and Optional Sections A 'typical' semester has 43 MWF days; a day or so will be lost to course-instructor evaluations, etc. The syllabus contains material for 40 days; you cannot afford to lose class periods. Those teaching on TTh should adjust the syllabus; a MWF lecture lasts 50 min;  TTh lecture lasts 75 min.

Forty Class Days As:

  • 5 Integrals (Seven Days)
    • 4.9 Antiderivatives (review)
    • 5.1 Areas and Distances
    • 5.2 The Definite Integral
    • 5.3 The Fundamental Theorem of Calculus
    • 5.4 Indefinite Integrals and the Net Change Theorem
    • 5.5 The Substitution Rule
  • 6 Applications of Integration (Two Days)
    • 6.1 Areas between Curves
    • 6.2 Volumes
  • 7 Inverse Functions: Exp Log and Inverse Trig (Three Days)
    • 7.2 Exponential Functions Their Derivatives (material with integrals)
    • 7.4 Derivatives of Logarithmic Functions (material with integrals)
    • 7.5 Inverse Trigonometric Functions (material with integrals)
    • 7.8 Indeterminate Forms and L'Hospital's Rule (review)
  • 8 Techniques of Integration (Seven Days)
    • 8.1 Integration by Parts
    • 8.2 Trigonometric Integrals
    • 8.3 Trigonometric Substitution
    • 8.4 Integration of Rational Functions by Partial Fractions
    • 8.5 Strategy for Integration
    • 8.7 Approximate Integration (optional)
    • 8.8 Improper Integrals
  • 15 Partial Derivatives (One Day)
    • 15.3 Partial Derivatives
  • 16 Multiple Integrals (Three Days)
    • 16.1 Double Integrals over Rectangles
    • 16.2 Iterated Integrals
    • 16.3 Double Integrals over General Regions
  • 12 Infinite Sequences and Series (Sixteen Days)
    • 12.1 Sequences
    • 12.2 Series
    • 12.3 The Integral Test and Estimates of Sums
    • 12.4 The Comparison Tests
    • 12.5 Alternating Series
    • 12.6 Absolute Convergence and the Ratio and Root Tests
    • 12.7 Strategy for Testing Series
    • 12.8 Power Series
    • 12.9 Representations of Functions as Power Series
    • 12.10 Taylor and Maclaurin Series
    • 12.11 Applications of Taylor Polynomials




 

Back to course listing