### Spring 2016

• 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
• Lecture 11: February 8, 2016. Surface integrals
• Lecture 12: February 10, 2016. The Divergence Theorem
• 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
• 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
• Lecture 15: February 22, 2016. Line integrals and the gradient
• Lecture 16: February 24, 2016. Laplace's equation
• 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
• 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.