Mathematics 240 Standard Version Syllabus
Topics which are reviewed from Math 114 and Math 104 are
indicated in
parentheses . Chapter and section references are to the third edition of Zill
Cullen’s “Advanced Engineering Mathematics”.
(1) Linear Algebra . 3 weeks
| Chapter 8: Matrices | Core ProblemS | |
| (8.1) | Matrix Algebra | 3,12,13,15,18, 23,28,33,36,38 |
| (8.2) | Systems of Linear Algebraic Equations | 5,7,9,20 |
| (8.3) | Rank of a Matrix | 1,5,9,13,16,17 |
| (8.4) | Determinants | 3,7,21,29 |
| (8.5) | Properties of Determinants | 4,7,12,15,21, 31,33,37,39 |
| (8.6) | Inverse of a Matrix | 1,5,9,11,21,25, 27,49,51 |
| (8.6.1) Finding the Inverse | ||
| (8.6.2) Using the Inverse to Solve Systems | ||
| (8.7) | Cramer’s rule (optional) | 1,9,11 |
| (8.8) | The Eigenvalue Problem | 1,6,7,15,21,26 |
| (8.12) | Diagonalization (optional) | 5,15,19,37 |
(2) Higher- Order Differential Equations. 2.5 weeks
| Chapter 3: Higher Order differential equations . | ||
| (3.1) | Preliminary Theory : Linear Equations | 1,3,7,15,18,22, 31,33,36 |
| (3.1.1) Initial- Value and Boundary Value Problems | ||
| (3.1.2) Homogeneous Equations | ||
| (3.1.3) Nonhomogeneous Equations | ||
| (3.3) | Homogeneous Linear Equations with Constant Coefficients | 3,15,37 |
| (3.4) | Undetermined Coefficients | 1,6,17,25,27,33 |
| (3.8) | Linear Models : Initial Value Problems | 3,7,17,25,31,43 |
| (3.8.1) Spring/Mass System: Free Undamped Motion | ||
| (3.8.2) Spring/Mass Systems: Free Damped Motion | ||
| (3.8.3) Spring/Mass System: Driven Motion | ||
| (3.6) | Cauchy-Euler Equation | 1,9,11,15,27 |
(3) Systems of Differential Equations. 2.5 weeks
| Chapter 10: Systems of Linear Differential Equations | ||
| (10.1) | Preliminary Theory | 5,7,13,19,25 |
| (10.2) | Homogeneous Linear Systems | 5,11,16,21 |
| (10.2.1) Distinct Real Eigenvalues | ||
| (10.2.2) Repeated Eigenvalues | ||
| (10.2.3) Complex Eigenvalues | ||
| (10.3) | Solutions by Diagonalization (optional) | 1,5,10 |
| (10.4) | Nonhomogeneous Linear Systems (optional) | 3,6,10 |
| (10.4.1) Undetermined Coefficients (optional) | ||
(4) Series Solutions. 1.5 weeks
| Chapter 5: Series Solutions of linear differential equations. | ||
| (5.1) | Solutions about Ordinary Points | 3,9,11,15,21,31 |
| (5.1.1) Review of Power series | ||
| (5.1.2) Power Series Solutions | ||
| (5.2) | Solutions about Singular Points | 5,11,15,21,27,33 |
| (5.3) | Special Functions | 1,5,9,11,15,18, 25,33,44 |
| (5.3.1) Bessel Functions | ||
| (5.3.2) Legendre Functions | ||
(5) Multivariable Calculus. 3.5 weeks
| Chapter 9: Vector Calculus | |
| (9.1) Vector Functions | 3,7,13,15,17,23, 25,29,33,39 |
| (9.4) Partial Derivatives (review) | 13,27,33,39,49,53 |
| (9.5) Directional Derivatives (review) | 1,11,16,23,27,31 |
| (9.6) Tangent Planes and Normal Lines (review) | 1,15,25,30 |
| (9.7) Divergence and Curl | 1,9,13,27,33,39 |
| (9.8) Line Integrals (review)(9.9) Independence of Path (review) | 1,2,7,19,21,23,28 |
| (9.9) Independence of Path (review) | 1,3,5,7,10,21,25, 27,31 |
| (9.10)Double Integrals (review) | 1,11,13,23,29,35, 40 |
| (9.11)Double Integrals in Polar Coordinates (review) | 1,5,8,20,25,28,32 |
| (9.12)Green’s theorem (review) | 1,5,10,13,18,21, 24,26,29 |
| (9.13)Surface integrals | 1,5,11,19,27,33, 37 |
| (9.14)Stokes’ Theorem | 1,3,5,11,15,17 |
| (9.15)Triple Integrals (review) | 1,4,7,9,12,13,15,19,21 |
| (9.16)Divergence Theorem | 3,7,11,15,17 |
| (9.17) Change of Variables in Multiple Integrals (review) | 1,3,5,11,17,25 |
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