Syllabus: M408C

DIFFERENTIAL AND INTEGRAL CALCULUS

Text: Stewart, Calculus, Early Transcendentals, Seventh Edition


Responsible Parties: Jane Arledge, Kathy Davis, Ray Heitmann June 2011

Prerequisite and degree relevance: Prerequisite is the minimum required score on the ALEKS placement exam.

Math majors are required to take both M408C and M408D (or either the equivalent sequence M408K, M408L, M408M; or the equivalent sequence M408N, M408S, M408M). Mathematics majors are required to make grades of C- or better in each of these courses.

408C may not be counted by students with credit for any of Mathematics 403K, 408K, 408N, or 408L.

Course description: M408C is the standard first-semester calculus course. It is directed at students in the natural sciences and engineering. The emphasis in this course is on problem solving, not the theory of analysis. There should be some understanding of analysis, but the majority of the proofs in the text should not be covered in class.

The syllabus for M408C includes most of the basic topics in the theory of functions of a real variable: algebraic, trigonometric, logarithmic and exponential functions and their limits, continuity, derivatives, maxima and minima, integration, area under a curve, volumes of revolution, and techniques of integration.

Overview and Course Goals

The following pages comprise the syllabus for M408C, and advice on teaching it. Calculus is a service course, and the material in it was chosen after interdepartmental discussions. Please do not make drastic changes (for example, skipping techniques of integration). You will do your students a disservice and leave them ill equipped for subsequent courses.

Remember that 408C/D is the fast sequence for students with good algebra skills; students who cannot maintain the pace are encouraged to take either the 408NSM or the 408KLM sequence.

Resources for Students

Many students find the study skills from high school are not sufficient for UT. Sanger Learning Center in Jester has a wide variety of material ( drills, video-taped lectures, computer programs, counseling, math anxiety workshops, algebra and trig review, calculus review) as well as tutoring options, all designed to help students through calculus. On request, (471-3614) they will come to your classroom and explain their services.

You can help your students by informing them of SLC services.

Timing and Optional Sections

A typical semester has 43 MWF days; a day or so will be lost to placement exams, etc. The syllabus contains material for 39 days; you cannot afford to lose class periods. If you plan to give exams in lecture rather than in TA section, you will surely have to cut time somewhere. We have added some flexibility to the syllabus by designating all the application sections as optional. It is expected that you will choose three or four of these and cover them well; it is unlikely that you will have time to cover all.

Those teaching on TTh should adjust the syllabus; a MWF lecture lasts 50 min; a TTh 75 min.

Forty Class Days As:



1 Functions and Models (Three Days )

  • 1.5 Exponential Functions
  • 1.6 Inverse Functions and Logarithms



2 Limits and Derivatives (Five Days)

  • 2.1 The Tangent and Velocity Problems
  • 2.2 The Limit of a Function
  • 2.3 Calculating Limits Using the Limit Laws
  • 2.4 The Precise Definition of a Limit (briefly)
  • 2.5 Continuity
  • 2.6 Limits at Infinity; Horizontal Asymptotes
  • 2.7 Derivatives and Rates of Change
  • 2.8 The Derivative of a Function



3 Differentiation Rules (Ten Days)

  • 3.1 Derivatives of Polynomials and Exonential Functions
  • 3.2 The Product and Quotient Rules
  • 3.3 Derivatives of Trigonometric Functions
  • 3.4 The Chain Rule
  • 3.5 Implicit Differentiation
  • 3.6 Derivatives of Logarithmic Functions
  • 3.7 Rates of Change in the Natural and Social Sciences (optional)
  • 3.8 Expontial Growth and Decay (optional)
  • 3.9 Related Rates (optional, but either this and/or 4.7 must be covered )
  • 3.10 Linear Approximations and Differentials (optional)
  • 3.11 Hyperbolic Functions(very quickly)



4 Applications of Differentiation (Seven Days)

  • 4.1 Maximum and Minimum Values
  • 4.2 The Mean Value Theorem
  • 4.3 How Derivatives Affect the Shape of a Graph
  • 4.4 Indeterminate Forms and L'Hospital's Rule
  • 4.5 Summary of Curve Sketching
  • 4.7 Optimization Problems (optional, but either this and/or 3.9 must be covered )
  • 4.9 Antiderivatives


5 Integrals (Five Days)

  • 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 Volume


7 Techniques of Integration (Seven Days)

  • 7.1 Integration by Parts
  • 7.2 Trigonometric Integrals
  • 7.3 Trigonometric Substitution
  • 7.4 Integration of Rational Functions by Partial Fractions (lightly)
  • 7.5 Strategy for Integration (for student reference)

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