- 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 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