Syllabus for Physics 155: Mathematical and Computational Methods
Spring 2016
Books for reading list
- Toeplitz, The Calculus: A Genetic Approach
- Shey, Div, Grad, Curl, and All That
- Marsden and Hoffman, Basic Complex Analysis
- Dettman, Introduction to Linear Algebra and Differential Equations
- Millman and Parker, Elements of Differential Geometry
- Seeley, An Introduction to Fourier Series and Integrals
Lecture list
- Lecture 1: January 13, 2016.
Irrational numbers, the Zeno effect, and the meaning of Pi
- Reading:
The Calculus: A Genetic Approach pp.1--22.
- Laboratory A: January 14, 2016.
Introduction to python. The many ways to calculate exp(x). Introduction to plotting with python.
- Preparation before lab:
Install Enthought's canopy on your computer. Instructions found on the EdX course page. Bring your computer to class with python ready to go.
- Lecture 2: January 15, 2016.
Everything you ever wanted (or did not want) to know about series.
- Reading:
The Calculus: A Genetic Approach pp. 22--42.
- Martin Kuther King Day (no class) January 18, 2016.
- Lecture 3: January 20, 2016.
Integrals, areas, and limits.
- Reading:
The Calculus: A Genetic Approach pp. 43--76.
- Laboratory B: January 21, 2016.
Numerical quadrature.
- Lecture 4: January 22, 2016.
Tangents and logarithms
- Reading:
The Calculus: A Genetic Approach pp. 77--94.
- January 22 is the last day for ADD/DROP!
- Lecture 5: January 25, 2016.
The Fundamental Theorem of Calculus and General Manipulations of Integrals
- Reading:
The Calculus: A Genetic Approach pp. 95--112.
- Lecture 6: January 27, 2016.
Examples of Integration including the Gaussian integral
- Reading:
The Calculus: A Genetic Approach pp. 113--132.
- Laboratory C: January 28, 2016.
What changes of variables are REALLY used for
- Lecture 7: January 29, 2016.
Multivariable integration: cubic, cylindrical, and spherical coordinates
- Lecture 8: February 1, 2016.
Multivariable integration: the vanishing sphere and other examples
- Lecture 9: February 3, 2016.
Feynman integration
- Reading: Handout on Feynman (or parametric) integration
- Laboratory D: February 4, 2016.
Moments of Inertia
- Lecture 10: February 5, 2016.
Vector-valued functions
- Reading:
Div, Grad, Curl, and All That pp. 1--8.
- Lecture 11: February 8, 2016.
Surface integrals
- Reading:
Div, Grad, Curl, and All That pp. 12--37.
- Lecture 12: February 10, 2016.
The Divergence Theorem
- Reading:
Div, Grad, Curl, and All That pp. 37--52.
- Laboratory E: February 11, 2016.
One-dimensional root finding and more practice with plotting
- Lecture 13: February 12, 2016.
The Line Integral and the Curl
- Reading:
Div, Grad, Curl, and All That pp. 63--86.
- President's Day (no class) February 15, 2016.
- Midterm 1: Calculus Review: February 17, 2016.
- Laboratory F: February 18, 2016.
Integral theorem examples
- Lecture 14: February 19: 2016.
Stokes Theorem
- Reading:
Div, Grad, Curl, and All That pp. 86--104.
- Lecture 15: February 22, 2016.
Line integrals and the gradient
- Reading:
Div, Grad, Curl, and All That pp. 115--124.
- Lecture 16: February 24, 2016.
Laplace's equation
- Reading:
Div, Grad, Curl, and All That pp. 124--141
- Laboratory G: February 25, 2016.
The relaxation method for solving Laplace's equation
- Lecture 17: February 26, 2016.
The Laplacian in cylindrical and spherical coordinates
- Reading:
Div, Grad, Curl, and All That pp. 141--144.
- Lecture 18: February 29, 2016.
Complex numbers and power series
- Reading:
Introduction to Linear Algebra and Differential Equations Chapter 1.
- Lecture 19: March 2, 2016.
Contour integration and the residue theorem
- Laboratory H: March 3, 2016.
Contour integrals, residues, and line integrals
- Lecture 20: March 4, 2016.
More examples of the residue theorem
- Spring break (no class) March 7--11, 2016
- Lecture 21: March 14, 2016.
Matrices and Gaussian elimination
- Reading:
Introduction to Linear Algebra and Differential Equations Chapter 2.1-2.3
- Lecture 22: March 16, 2016.
Determinants
- Reading:
Introduction to Linear Algebra and Differential Equations Chapter 2.4.
- Laboratory I: March 17, 2016.
Row reduction and partial pivoting
- Lecture 23: March 18, 2016.
Inverse of a Matrix
- Reading:
Introduction to Linear Algebra and Differential Equations Chapter 2.5.
- Lecture 24: March 21, 2016.
Vector Spaces
- Reading:
Introduction to Linear Algebra and Differential Equations Chapter3.1-3.6.
- Last day to drop the class is March 22, 2016.
- Midterm II: Multivariable calculus and integral theorems. March 23, 2016.
- Easter Break (no class) March 24--28, 2016.
- Lecture 25: March 30, 2016.
Scalar products and orthonormality
- Reading:
Introduction to Linear Algebra and Differential Equations Chapter 3.7.
- Laboratory J: March 31, 2016.
Gram-Schmidt orthogonality and the van der Monde determinant
- Lecture 26: April 1, 2016.
Change of bases
- Reading:
Introduction to Linear Algebra and Differential Equations Chapter 4.1-4.4.
- Lecture 27: April 4, 2016.
Eigenvalues and Eigenvectors
- Reading:
Introduction to Linear Algebra and Differential Equations Chapter 4.5-4.6.
- Lecture 28: April 6, 2012.
Physics examples of eigenvalues and eigenvectors
- Laboratory K: April 7, 2016.
Eigenvalues and determinants
- Lecture 29: April 8, 2016.
First-order ordinary differential equations (Linear)
- Reading:
Introduction to Linear Algebra and Differential Equations Chapter 5.1-5.4.
- Lecture 30: April 11, 2016.
First-order ordinary differential equations (Nonlinear)
- Reading:
Introduction to Linear Algebra and Differential Equations Chapter 5.5.
- Lecture 31: April 13, 2016.
Physics examples of first-order differential equations
- Reading:
Introduction to Linear Algebra and Differential Equations Chapter 5.6.
- Laboratory L: April 14, 2016.
Solving ordinary differential equations
- Reading:
Introduction to Linear Algebra and Differential Equations Chapter 5.7.
- Lecture 32: April 15, 2016.
Introduction to linear differential equations
- Reading:
Introduction to Linear Algebra and Differential Equations Chapter 6.1-6.3.
- Lecture 33: April 18, 2016.
Differential equations with constant coefficients
- Reading:
Introduction to Linear Algebra and Differential Equations Chapter 6.4.
- Lecture 34: April 20, 2014.
Method of undetermined coefficients and applications
- Reading:
Introduction to Linear Algebra and Differential Equations Chapter 6.5-6.6.
- Laboratory M: April 21, 2016.
Solving second order differential equations
- Lecture 35: April 22, 2016.
Frenet-Serret Apparatus
- Reading:
Elements of Differential Geometry pp. 13-35.
- Lecture 36: April 25, 2016.
The Dirichlet problem and Fourier Series
- Reading:
An Introduction to Fourier Series and Integrals pp. 1--27.
- Midterm III: Matrices and first order differential equations April 27, 2014.
- Laboratory N: April 28, 2014.
Newton's method of orbits
- Lecture 37: April 29, 2016.
Separation of Variables
- Reading:
An Introduction to Fourier Series and Integrals pp. 29--41.
- Lecture 38: May 2, 2016
Applications of Poisson's Theorem
- Reading:
An Introduction to Fourier Series and Integrals pp. 42--53.
- Final Exam: Saturday, May 7, 2016 (2:00-4:00 pm). Location TBA.
Last modified January 8, 2016.
Jim Freericks, Professor of Physics,
freericks at physics dot georgetown dot edu