Math 235. Accelerated Calculus I (formerly Math 135)
Syllabus for Lecture-Discussion Form
Text: Salas, Hille and Etgen, Calculus: One and Several Variables, 8th Edition, Wiley, 1999.
- Chapter 1: Introduction (5 days)
- 1.1 What is Calculus (0)
- 1.2 Notations and Formulas from Elementary Mathematics (.5)
- 1.3 Inequalitities (.5)
- 1.4 Coordinate Plane; Analytic Geometry (.5)
- 1.5 Functions (.5)
- 1.6 Elementary Functions (.5)
Exponential and Logarithmic Functions from Notes (.5) - 1.7 Combinations of Functions (1)
- 1.8 A Note on Mathematical Proof: Mathematical Induction (1)
- Chapter 2: Limits and Continuity (7 days)
- 2.1 The Idea of Limit (1)
- 2.2 Definition of Limit (1)
- 2.3 Some Limit Theorems (1.5)
- 2.4 Continuity (1)
- 2.5 The Pinching Theorem: Trigonometric Limits (1)
- 2.6 Two Basic Theorems (Infinity/Infinity), etc. (1.5)
- Chapter 3: Differentiation (11 days)
- 3.1 The Derivative (1)
- 3.2 Some Differentiation Formulas (2)
- 3.3 The d/dx Notation; Derivatives of Higher Order (1)
- 3.4 The Derivative as a Rate of Change (1)
- 3.5 The Chain Rule (1)
- 3.6 Differentiating the Trigonometric Functions (1)
- 3.7 Implicit Differentiation; Rational Powers (1)
- 3.8 Rates of Change Per Unit Time (1)
- 3.9 Differentials; Newton-Raphson Approximations (2)
- Chapter 4: The Mean-Value Theorem and Applications (9 days)
- 4.1 The Mean-Value Theorem (1)
- 4,2 Increasing and Decreasing Functions (1)
- 4.3 Local Extreme Values (1)
- 4.4 Endpoint and Absolute Extreme Values (1)
- 4.5 Some Min-Max Problems (12
- 4.6 Concavity and Points of Inflection (1)
- 4.7 Vertical and Horizontal Asymptotes; etc. (1)
- 4.8 Curve Sketching (1)
- Chapter 5: Integration (13 days)
- 5.1 The Definite Integral of a Cont. Function (2.5)
- 5.2 The Function F(x) = integral from a to x f (t) d t (1)
- 5.3 The Fundamental Theorem of Integral Calculus (1.5)
- 5.4 Some Area Problems (1)
- 5.5 Indefinite Integrals (1.5)
- 5.6 Substitution and Change of Variables (1.5)
- 5.7 Some Further Properties of the Definite Integral (1)
- 5.8 Mean-Value Theorem of Integrals and Averages (1)
- 8.7 Numerical Integration FROM CHAPTER 8 (2)
- Chapter 6: Some Applications of the Integral (5 days)
- 6.1 More on Area (1)
- 6.2 Volume by Parallel Cross-Sections; Discs and Washers (2)
- 6.3 Volume by the Shell Method (omit)
- 6.4 The Centroid of a Region; Pappus's Theorem on Volumes (omit)
- 6.5 The Notion of Work (1)
- 6.6 Fluid Pressure and Fluid Forces (1)
- Chapter 7: The Transcendental Functions (10 days)
- 7.1 The One-To-One Functions; Inverses (1)
- 7.2 The Logarithm Function, Part 1 (1)
- 7.3 The Logarithm Function, Part 2 (2)
- 7.4 The Exponential Function (1)
- 7.5 Arbitrary Powers; Other Bases; Estimating e (1)
- 7.6 Exponential Growth and Decay (1.5)
- 7.7 The Inverse Trigonometric Functions (1.5)
- 7.8 The Hyperbolic Sine and Cosine (1)
- 7.9 The Other Hyperbolic Functions (omit)
- Chapter 8: Techniques of Integration (6 days)
- 8.1 Review (1)
- 8.2 Integration by Parts (1.5)
- 8.3 Powers and Products of Trigonometric Functions (2.5)
- 8.4 Trig Substitution (1)
- 8.5 Partial Fractions (if time permits)
- 8.6 Some Rationalizing Substitutions (omit)
- 8.7 Numerical Integration (done before)
- 8.8 Differential Equations (omit)
- 8.9 Separable Equations (omit)
- Exams (4 days)
- Review and Leeway (4 days)
- Total (74 days)
Last modified 5/22/02