Math 245. Accelerated Calculus II
Syllabus for Lecture-Discussion Form of Math 245

Text: Salas, Hille and Etgen, Calculus: One and Several Variables, 8th Edition, Wiley, 1999.

• Chapter 9: The Conic Sections; Polar Coordinates; Parametric Equations (7 days)
  • 9.1, 9.2 Conic Sections (2)
  • 9.3 Polar Coordinates (.5)
  • 9.4 Graphing in Polar Coordinates (1)
  • 9.5 Area in polar coordinates (1)
  • 9.6 Curves Given Parametrically (1)
  • 9.7 Tangents to Curves Given Parametrically (.5)
  • 9.8 Arc Length and Speed (1)
  • 9.9 Area of a Surface of Revolution, etc. (omit)

• Chapter 10: Sequences, Indeterminate Forms, Improper Integrals (7 days)
  • 10.1 Least Upper Bound Axiom (1)
  • 10.2 Sequences of Real Numbers (1)
  • 10.3 Limit of a Sequence (1)
  • 10.4 Some Important Limits (1)
  • 10.5 The Indeterminate Form (0/0) (.5)
  • 10.6 The Indeterminate Form (infinity/infinity), etc. (.5)
  • 10.7 Improper Integrals (2)

• Chapter 11: Infinite Series (10 days)
  • 11.1 Infinite Series (1)
  • 11.2 The Integral Test; Comparison Theorems (1)
  • 11.3 The Root Test; The Ratio Test (1)
  • 11.4 Absolute and Conditional Convergence; Alternating Series (1)
  • 11.5 Taylor Polynomials in x, etc. (2)
  • 11.6 Taylor Polynomial and Taylor Series in x - a (1)
  • 11.7 Power Series (1)
  • 11.8 Differentiation and Integration of Power Series (2)
  • 11.9 The Binomial Series (omit)

• Chapter 12: Vectors (7 days)
  • 12.1 Cartesian Space Coordinates (1)
  • 12.2, 12.3 Displacements, etc.; Vectors (1)
  • 12.4 The Dot Product (1)
  • 12.5 The cross product (1)
  • 12.6 Lines (1.5)
  • 12.7 Planes (1.5)

• Chapter 13: Vector Calculus (6 days)
  • 13.1 Vector Functions (1)
  • 13.2 Differentiation Formulas (1)
  • 13.3 Curves (1.5)
  • 13.4 Arc Length (1)
  • 13.5 Curvilinear Motion, etc (.5, omit vector mechanics)
  • 13.6 Planetary Motion (omit)
  • 13.7 Curvature (1)

• Chapter 14: Functions of Several Variables (5 days)
  • 14.1 Elementary Examples (.5)
  • 14.2 . . ., Quadric Surfaces (1)
  • 14.3 Graphs, Level Curves and Level Surfaces (.5)
  • 14.4 Partial Derivatives (1.5)
  • 14.5 Open Sets and Closed Sets (.5)
  • 14.6 Limits and Continuity; Equality of Mixed Partials (1)
  
  
• Chapter 15: Gradients; Extreme Values; Differentials (12 days)
  
  • 15.1 Differentiability and Gradient (1.5)
  • 15.2 Gradients and Directional Derivatives (1.5)
  • 15.3 The Mean-Value Theorem, Chain Rules (2)
  • 15.4 The Gradient as a normal, . . . (1)
  • 15.5 Maximum and Minimum Values (2)
  • 15.6 Maxima and minima with side conditions(2)
  • 15.7 Differentials (1)
  • 15.8 Reconstructing a funciton from its gradient (1)
  • 15.9 Exact Differential Equations (omit)
  
  
• Chapter 16: Double and Triple Integrals (12 days)
  • 16.1 Multiple Sigma Notation (.5)
  • 16.2 The Double Integrals (1)
  • 16.3 The Evaluation of Double Integrals by Repeated Integrals (1.5)
  • 16.4 The Double Integral as the Limit of Riemann Sums, . . . (1.5)
  • 16.5 Some Applications of Double Integration (1)
  • 16.6 Triple Integrals (.5)
  • 16.7 Reduction to Repeated Integrals (2)
  • 16.8 Cylindrical Coordinates (1)
  • 16.9 . . .; Spherical Coordinates (1.5)
  • 16.10 Jacobians; . . . (1.5)
  
  
• Exams (4 days)
  
• Review and Leeway (4 days)
  
• Total (74 days)

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