| 1 |
Course Organization and Introduction to Mathematica®, Assignment and Evaluation |
Lecture Notes only |
| 2 |
Introduction and Overview of Mathematica®, Assignment and Evaluation, Mathematica® Functions, Operations on Expressions, Lists, Getting Help |
Lecture Notes only |
| 3 |
Procedural and Functional Programming, Functions and Rules |
Lecture Notes only |
| 4 |
Mathematica®: Symbolic and Numeric Calculations, Roots of Equations, File Input and Output |
Lecture Notes only |
| 5 |
Mathematica® Graphics: Plotting Data, Two- and Three-Dimensional Plotting, Graphics Primitives |
Lecture Notes only |
| 6 |
Linear Algebra: Matrix Operations, Interpretations of Matrix Operations, Multiplication, Transposes, Index Notation |
Kreyszig: 6.1, 6.2, 6.3, 6.4
(pages: 304–309, 312–318, 321–323, 331–336) |
| 7 |
Linear Algebra: Solutions to Linear Systems of Equations, Determinants, Matrix Inverses, Linear Transformations and Vector Spaces |
Kreyszig: 6.5, 6.6, 6.7, 6.8
(pages: 338–341, 341–347, 350–357, 358–364) |
| 8 |
Complex Numbers: Complex Plane, Addition and Multiplication, Complex Conjugates, Polar Form of Complex Numbers, Powers and Roots, Exponentiation, Hyperbolic and Trigonometric Forms |
Kreyszig: 12.1, 12.2, 12.6, 12.7
(pages: 652–656, 657–662, 679–682, 682–685) |
| 9 |
Matrix Eigenvalues: Eigenvalue/Eigenvector Definitions, Invariants, Principal Directions and Values, Symmetric, Skew-symmetric, and Orthogonal Systems, Orthogonal Transformations |
Kreyszig: 7.1, 7.2, 7.3
(pages: 371–375, 376–379, 381–384) |
| 10 |
Hermitian Forms, Similar Matrices, Eigenvalue Basis, Diagonal Forms |
Kreyszig: 7.4, 7.5
(pages: 385–389, 392–396) |
| 11 |
Vector Calculus: Vector Algebra, Inner Products, Cross Products, Determinants as Triple Products, Derivatives of Vectors |
Kreyszig: 8.1, 8.2, 8.3, 8.4
(pages: 401–406, 408–413, 414–421, 423–427) |
| 12 |
Multi-variable Calculus: Curves and Arc Length, Differentials of Scalar Functions of Vector Arguments, Chain Rules for Several Variables, Change of Variable and Thermodynamic Notation, Gradients and Directional Derivatives |
Kreyszig: 8.5, 8.8, 8.9
(pages: 428–433, 444–446, 446–452) |
| 13 |
Vector Differential Operations: Divergence and Its Interpretation, Curl and Its Interpretation |
Kreyszig: 8.10, 8.11
(pages: 453–456, 457–459) |
| 14 |
Path Integration: Integral Over a Curve, Change of Variables, Multidimensional Integrals |
Kreyszig: 9.1, 9.2, 9.3
(pages: 464–470, 471–477, 478–484) |
| 15 |
Multidimensional Forms of the Fundamental Theorem of Calculus: Green’s Theorem in the Plane, Surface Representations and Integrals |
Kreyszig: 9.4, 9.5, 9.6, 9.7
(pages: 485–490, 491–495, 496–505, 505-509) |
| 16 |
Multi-variable Calculus: Triple Integrals and Divergence Theorem, Applications and Interpretation of the Divergence Theorem, Stoke’s Theorem |
Kreyszig 9.8, 9.9 (pages: 510-514, 515-520) |
| 17 |
Periodic Functions: Fourier Series, Interpretation of Fourier Coefficients, Convergence, Odd and Even Expansions |
Kreyszig 10.1, 10.2, 10.3, 10.4 (pages: 527-528, 529-536, 537-540, 541-546) |
| 18 |
Fourier Theory: Complex Form of Fourier Series, Fourier Integrals, Fourier Cosine and Sine Transforms, The Fourier Transforms |
Kreyszig 10.5, 10.8, 10.9, 10.10 (pages: 547-549, 557-563, 564-568, 569-575) |
| 19 |
Ordinary Differential Equations: physical interpretations, geometrical interpretations, separable equations |
Kreyszig 1.1, 1.2, 1.3 (pages: 2-8, 10-12, 14-18) |
| 20 |
ODEs: Derivations for Simple Models, Exact Equations and Integrating Factors, The Bernoulli Equation |
Kreyszig: 1.4, 1.5, 1.6
(pages: 19–22, 25–31, 33–38) |
| 21 |
Higher Order Differential Equations: Homogeneous Second Order, Initial Value Problems, Second Order with Constant Coefficients, Solution Behavior |
Kreyszig: 2.1, 2.2, 2.3
(pages: 54–70, 72–75, 76–80) |
| 22 |
Differential Operators, Damped and Forced Harmonic Oscillators, Nonhomogeneous Equations |
Kreyszig: 2.4, 2.5, 2.8
(pages: 81–83, 83–89, 101–103) |
| 23 |
Resonance Phenomena, Higher Order Equations, Beam Theory |
Kreyszig: 2.11, 2.13 (beam theory only)
(pages: 111–116, 130–131) |
| 24 |
Systems of Differential Equations, Linearization, Stable Points, Classifi-cation of Stable Points |
Kreyszig: 3.1, 3.2
(pages: 152–157, 159–161) |
| 25 |
Linear Differential Equations: Phase Plane Analysis and Visualization |
Kreyszig: 3.3, 3.4
(pages: 161–169, 170–174) |
| 26 |
Solutions to Differential Equations: Legendre’s Equation, Orthogonality of Legendre Polynomials, Bessel’s Equation and Bessel Functions |
Kreyszig: 4.3, 4.5, 4.6
(pages: 111–116, 130–131, 228–232) |
| 27 |
Sturm-Louiville Problems: Eigenfunction, Orthogonal Functional Series, Eigenfunction Expansions |
Kreyszig: 4.7, 4.8
(pages: 233–238, 240–248) |
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