Timetable Math 21a Fall 2000
Math 21 a Math21a, Fall 2000 Course Head: Prof. Clifford H. Taubes
Dini surface: surface of constant negative curvature

Math 21a Fall 2000 Syllabus Outline

Regular Sections
Textbook: "Multivariable Calculus with the Student Solutions Manual" by Ostebee and Zorn,

  1. Section 1.1: 3-d space and surface.
  2. Section 1.2: Parametric curves.
  3. Section 1.3-1.4: Vectors, vector valued functions.
  4. Section 1.5: Derivatives, anti-derivatives and motion.
  5. Sections 1.6-1.7: Dot product, lines and planes
  6. Sections 1.7-1.8: Lines, planes and cross product.
  7. Appendix C: Introduction to matrices.
  8. Sections 2.1 and 1.1: Functions of several variables.
  9. Sections 2.2-2.3: Partial derivatives, contours and linear approximations.
  10. Sections 2.3-2.4: Linear approximations and the gradient.
  11. Sections 2.5-2.6: Theory of derivatives, high order derivatives and quadratic approx.
  12. Section 2.7: Max-min, critical points and extreme points.
  13. Sections 2.7 and 4.4: More on extreme points, constrained optimization.
  14. Section 4.4: Constrained opimization.
  15. Section 2.8: Multivariable chain rule.
  16. Section 3.1: Multiple integrals.
  17. Section 3.2: Calculating integrals by iteration.
  18. Section 3.3: Integrals in polar coordinates.
  19. Section 3.4: Integrals in spherical and cylindrical coordinates.
  20. Section 5.1: Line integrals and vector fields.
  21. Section 5.2: The fundamental theorem of line integrals.
  22. Section 5.3: Line integrals and Green's theorem.
  23. Section 5.4: Surfaces and parameterizations.
  24. Section 5.5: Surface integrals
  25. Section 5.6: Derivatives of vector valued functions, div and curl.
  26. Section 5.7: Stoke's theorem.
  27. Section 5.7: Divergence theorem.
  28. Section 5.7: More on Stoke's and Divergence Theorems.
  • Handouts: Differential equations.
  • Various computer assignments.
  • Two "midterm" exams: Wed., Oct. 18 and Wed., Nov. 15, both are from 7-9pm and in Science Center Lecture Halls C and D.
  • A final exam scheduled by the University; the preliminary date is Sat., Jan. 13 in the morning.
Physics Sections
Textbook: "Multivariable Calculus with the Student Solutions Manual" by Ostebee and Zorn

  1. Section 1.1: 3-d space and surface.
  2. Section 1.2: Parametric curves.
  3. Section 1.3-1.4: Vectors, vector valued functions.
  4. Section 1.4-1.5: Derivatives, anti-derivatives and motion.
  5. Sections 1.6-1.7: Dot product, lines and planes
  6. Sections 1.7-1.8: Lines, planes and cross product.
  7. Sections 1.1, 2.1-2.2: Functions of several variables, partial derivative, gradients.
  8. Section 5.1: Line integrals and vector fields.
  9. Section 5.2: The fundamental theorem of line integrals.
  10. Section 2.3Linear approximations
  11. Section 2.4: The gradient and directional derivatives.
  12. Appendix C: Introduction to matrices.
  13. Sections 2.5-2.6: Theory of derivatives, high order derivatives and quadratic approx.
  14. Section 2.7: Max-min, critical points and extreme points.
  15. Sections 2.7 and 4.4: More on extreme points, constrained optimization.
  16. Section 4.4: Constrained opimization.
  17. Section 2.8: Multivariable chain rule.
  18. Section 3.1: Multiple integrals.
  19. Section 3.2: Calculating integrals by iteration.
  20. Section 3.3: Integrals in polar coordinates.
  21. Section 3.4: Integrals in spherical and cylindrical coordinates.
  22. Section 5.3: Line integrals and Green's theorem.
  23. Section 5.4: Surfaces and parameterizations.
  24. Section 5.5: Surface integrals
  25. Section 5.6: Derivatives of vector valued functions, div and curl.
  26. Section 5.7: Stoke's theorem.
  27. Section 5.7: Divergence theorem.
  28. Section 5.7: More on Stoke's and Divergence Theorems.
  29. Handouts: Differential equations.
  • Supplementary handouts: Work and Energy, Angular Momentum, Planetary Motion, Relativity, Center of Mass, Electricity and Magnetism, Euler's Equation, Wave Equations, Heat Equation, Laplace's Equation, Schrodinger's Equation, Dirac's Equation.
  • Various computer assignments.
  • Two "midterm" exams: Wed., Oct. 18 and Wed., Nov. 15, both from 7-9pm and in Science Center Lecture Halls C and D.
  • A final exam scheduled by the University; the preliminary date is Sat., Jan. 13 in the morning.
BioChem Sections
Textbooks:
  • "Multivariable Calculus with the Student Solutions Manual" by Ostebee and Zorn
  • "Fundamentals of Biostatistcs" by Rosner.

  1. Section 1.1: 3-d space and surface.
  2. Section 1.2: Parametric curves.
  3. Section 1.3-1.4: Vectors, vector valued functions.
  4. Section 1.5: Derivatives, anti-derivatives and motion.
  5. Sections 1.6-1.7: Dot product, lines and planes
  6. Sections 1.7-1.8: Lines, planes and cross product.
  7. Appendix C: Introduction to matrices.
  8. Sections 2.1 and 1.1: Functions of several variables.
  9. Sections 2.2-2.3: Partial derivatives, contours and linear approximations.
  10. Sections 2.3-2.4: Linear approximations and the gradient.
  11. Sections 2.5-2.6: Theory of derivatives, high order derivatives and quadratic approx.
  12. Section 2.7: Max-min, critical points and extreme points.
  13. Sections 2.7 and 4.4: More on extreme points, constrained optimization.
  14. Section 4.4: Constrained opimization.
  15. Section 2.8: Multivariable chain rule.
  16. Section 3.1: Multiple integrals.
  17. Section 3.2: Calculating integrals by iteration.
  18. Section 3.3: Integrals in polar coordinates.
  19. Section 3.4: Integrals in spherical and cylindrical coordinates.
  20. Rosner Chapter 2: Descriptive statistics.
  21. Rosner Chapter 3: Beginning probability including addition laws, multiplication laws, conditional probability, total probability, Bayes' theorem.
  22. Rosner Chapter 4: Discrete probability distributions including binomial distributions, Poisson distributions.
  23. Rosner Chapter 5: Continuous probability including density functions, mean and variance, normal distributions, approximation by normal distributions.
  24. Handouts: Differential equations.
  • Various computer assignments.
  • Two "midterm" exams: Wed., Oct. 18 and Wed., Nov. 15, both are from 7-9pm and in Science Center Lecture Halls C and D.
  • A final exam scheduled by the University; the preliminary date is Sat., Jan. 13 in the morning.
Course outline
Posted: 9/11/2000, math21a@fas.harvard.edu