MAT 267 Honors Calculus for Engineers III Vector Calculus
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Memorize! Topics for Test 1 Topics for Test 2 Topics for Test 3 Maxwell’s Equations Navier-Stokes Equations For Fun wave1.m wave2.m diffusion2D.m laplace1.m Homework Problems HW1 (due Fri 8/25) Vectors, Dot Products, Planes HW2 (due Fri 9/1) Cross Products, Lines, Planes, Parametric Curves HW3 (due Fri 9/8) Surfaces, Partial Derivatives, Heat Equation & Wave Equation HW4 (due Fri 9/15) Tangent & Normal Vector to Line, Tangent Plane & Normal Vector, Differentials, Linear Approx Practice Test 1 HW5 (due Wed 9/27) Directional Derivative & Gradient, Maxima/Minima/Saddle Points, Second Derivative Test HW6 (due Wed 10/4) Double Integrals in Cartesian & Polar Coordinates HW7 (due Fri 10/13) Triple Integrals in Cartesian, Cylindrical, & Spherical Coordinates HW8 (due Fri 10/20) Grad, Div, Curl; Vector Fields Practice Test 2 HW9 (due Fri 11/3) Line Integrals, Conservative Vector Fields HW10 (due Mon 11/13) Green’s Theorem/Stokes’ Theorem, Surface Integrals HW11 (due Mon 11/20) Gauss’ Divergence Theorem; Laplace’s Equation & Poisson’s Equation Practice Test 3 Lecture Notes (view on screen only--save a tree!) Vectors, Dot Product, Cross Product, Lines, Planes, Parametric Curves (Stewart Essential Calculus, Sections 10.1-10.5) Surfaces, Partial Derivatives, Heat Eq & Wave Eq (10.6-10.7, 11.3) [Heat Equation Fundamental Solution] [Classifying Linear PDEs] Arc Length, Curvature, Tangent Vector & Normal Vector to Line (10.8-10.9) Tangent Plane & Normal Vector, Differentials, Linear Approximation (11.1, 11.3-11.4) [ Example where fxy ≠ fyx (see also problem 11.3 83)] -------- Test 1 -------- Directional Derivative & the Gradient (11.6) Second Derivative Test Example Chain Rule, Maxima/Minima/Saddle Points, Taylor Series (11.5, 11.7) Taylor Series Formula for f(x,y) 3D Laplace Equation Solution Introduction to Multiple Integrals Double Integrals in Cartesian & Polar Coord’s (12.1-12.3) Triple Integrals in Cartesian, Cylindrical, & Spherical Coord’s (12.5-12.7) [Newton’s Gravitational Integral] Grad, Div, Curl (13.5) -------- Test 2 -------- Vector Fields, Line Integrals (13.1-13.3) Conservative Vector Fields (13.2-13.3) Four Fundamental Theorems of Vector Calculus Green’s Theorem (2D) (13.4) planimeter Intro to Gauss’ Divergence Theorem & Stokes’ Theorem Maxwell’s Equations Surface Integrals (13.6-13.7) Gauss’ Divergence Theorem (13.9) [Navier-Stokes Equations] Laplace’s Equation & Poisson’s Equation Review: Four Fundamental Theorems (Chapter 13) -------- Test 3 -------Using Wolfram Alpha Alpha Website A login for the PRO version (highly recommended) can be obtained from your MyASU > MyApps Useful Alpha Commands