Math 19: Calculus 2 for Physics and Engineering (Fall 2014)

A second-semester course in calculus, geared towards students interested in physics and engineering.

• Syllabus
• Topic schedule

Announcements

Textbook and readings

• Calculus by Gilbert Strang. This will be our primary text for the course. You can purchase it from the bookstore or use it online for free.

10/01 Complex nth roots Notes on finding complex solutions to an equation z^n=c.

10/15 Differential Equations Some topics in differential equations. This document is still being updated as we cover more material (last update, 10/16).

11/05 Convergence tests summary

11/07 Taylor Approximation.

Fourier Series by James Stewart.

Complex Fourier Series (focuses on the case of finite Fourier series, sometimes called trigonometric polynomials)

Fourier series and differential equations

Problem sets and solutions

Solutions will be posted after class on the due date of each assignment.

• Problem set 1 (due F 9/12). Review of Calculus 1; integration by parts; trigonometric integrals; trigonometric substitution.

  • Solutions

• Problem set 2 (due F 9/19). Force and energy; vectors.

  • Solutions

• Problem set 3 (due F 9/26). Paths in two and three dimensions; polar coordinates.

  • Solutions

• Problem set 4 (due F 10/3). Polar coordinates, complex numbers.

  • Solutions

• Problem set 5 (due F 10/17). Linear differential equations.

  • Solutions

• Problem set 6 (due F 10/24). Initial value problems; improper integrals; review of summation notation.

  • Solutions

• Problem set 7 (due M 11/3). Geometric series. Integral test.

  • Solutions

• Problem set 8 (due F 11/7). Convergence tests.

  • Solutions

• Problem set 9 (due M 11/24).

  • Solutions

• Problem set 10 (due M 12/8).

  • Solutions

Exams and solutions

• Topic list for the midterm 1.
• Practice Midterm 1 (Solutions)
• Midterm 1 (solutions)
• Practice Midterm 2(Solutions)
• Midterm 2 (Solutions)
• Final review problems 1 / Answers
• Final review problems 2 / Answers
• Practice Final Exam (Solutions)
• Final Exam (Solutions)

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Student notes

Students in the class have kindly provided their notes for the following lectures.

• 3 September (Integration by parts)
• 8 September (Resonance and trig. substitution)
• 12 September (Work and energy)
• 15 September (Vectors)
• 17 September (Paths)
• 19 September (Acceleration and g-force)
• 22 September (more) (Arc length, polar coordinates)
• 24 September (Polar curves)
• 26 September (Conic sections; area in polar coordinates)
• 29 September (Arc length in polar coordinates)
• 1 October (Complex numbers)
• 03 October (more) (Linear differential equations)
• 15 October (General solutions of differential equations)
• 17 October (Separable differential equations)
• 20 October (more) (Non-homogeneous linear differential equations)
• 22 October (more) (Improper integrals)
• 27 October (more) (Geometric series)
• 29 October (more) (Variations on geometric series; the integral test)
• 31 October (more) (Integral and comparison tests)
• 3 November (more) (Comparison and Ratio tests)
• 5 November (Alternating series test)
• 7 November (Linear and quadratic approximation)
• 10 November (Taylor approximation)
• 17 November (Taylor series)
• 19 November (Taylor series, cont.)
• 21 November (Fourier series)
• 24 November (Fourier series examples)
• 1 December (Fourier series examples)
• 3 December (Fourier series and differential equations)
• 5 December (Fourier series and differential equations)
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