Focus mode

Engineering Mathematics

Engineering Mathematics: ordinary and partial differential equations, Laplace and Fourier transforms, vector calculus, complex analysis, and numerical methods for solving engineering models.

0 of 58 modules completed0%

Saved in this browser

Start here

Classifying differential equations and initial value problemsStart module 1 Starting Check for this course (6 questions)

Grade University

0/58 completed

Up nextModule 1 · Ordinary Differential EquationsClassifying differential equations and initial value problems
Not startedModule 2 · Ordinary Differential EquationsDirection fields and the behavior of solutions
Not startedModule 3 · Ordinary Differential EquationsExistence, uniqueness, and the interval of a solution
Not startedModule 4 · Ordinary Differential EquationsSeparable equations
Not startedModule 5 · Ordinary Differential EquationsFirst-order ODEs and integrating factors
Not startedModule 6 · Ordinary Differential EquationsExact equations and integrating factors
Not startedModule 7 · Ordinary Differential EquationsBernoulli and homogeneous substitutions
Not startedModule 8 · Ordinary Differential EquationsGrowth, decay, and mixing
Not startedModule 9 · Ordinary Differential EquationsLogistic and autonomous models
Not startedModule 10 · Ordinary Differential EquationsHomogeneous equations with constant coefficients
Not startedModule 11 · Ordinary Differential EquationsThe Wronskian and fundamental sets of solutions
Not startedModule 12 · Ordinary Differential EquationsNonhomogeneous equations: undetermined coefficients
Not startedModule 13 · Ordinary Differential EquationsNonhomogeneous equations: variation of parameters
Not startedModule 14 · Ordinary Differential EquationsHigher-order linear equations
Not startedModule 15 · Ordinary Differential EquationsDamped second-order linear ODEs
Not startedModule 16 · Ordinary Differential EquationsForced vibrations and resonance
Not startedModule 17 · Ordinary Differential EquationsPower series solutions near an ordinary point
Not startedModule 18 · Ordinary Differential EquationsRegular singular points and the Frobenius method
Not startedModule 19 · Ordinary Differential EquationsBessel's and Legendre's equations
Not startedModule 20 · Ordinary Differential EquationsIntroduction to the Laplace transform
Not startedModule 21 · Ordinary Differential EquationsSolving initial value problems with the Laplace transform
Not startedModule 22 · Ordinary Differential EquationsThe Heaviside step function and the Dirac delta
Not startedModule 23 · Ordinary Differential EquationsSystems of differential equations (matrix methods)
Not startedModule 24 · Ordinary Differential EquationsLinear systems and elimination
Not startedModule 25 · Ordinary Differential EquationsFundamental matrices and the matrix exponential
Not startedModule 26 · Ordinary Differential EquationsNonhomogeneous systems and variation of parameters
Not startedModule 27 · Ordinary Differential EquationsThe phase plane and linearization
Not startedModule 28 · Ordinary Differential EquationsStability and basic Lyapunov functions
Not startedModule 29 · Advanced Vector CalculusScalar fields, vector fields, and the del (nabla) operator
Not startedModule 30 · Advanced Vector CalculusDivergence and curl
Not startedModule 31 · Advanced Vector CalculusLine integrals and work
Not startedModule 32 · Advanced Vector CalculusGreen's theorem and Stokes' theorem
Not startedModule 33 · Advanced Vector CalculusThe divergence theorem (Gauss's theorem)
Not startedModule 34 · Fourier Series and Partial Differential EquationsFourier series
Not startedModule 35 · Fourier Series and Partial Differential EquationsThe continuous Fourier transform
Not startedModule 36 · Fourier Series and Partial Differential EquationsTwo-point boundary value problems
Not startedModule 37 · Fourier Series and Partial Differential EquationsSturm–Liouville problems
Not startedModule 38 · Fourier Series and Partial Differential EquationsSeparation of variables
Not startedModule 39 · Fourier Series and Partial Differential EquationsThe one-dimensional heat equation
Not startedModule 40 · Fourier Series and Partial Differential EquationsThe one-dimensional wave equation
Not startedModule 41 · Applied Complex AnalysisComplex number algebra and phasors
Not startedModule 42 · Applied Complex AnalysisAnalytic functions and the Cauchy–Riemann equations
Not startedModule 43 · Applied Complex AnalysisComplex contour integration (Cauchy's integral theorem)
Not startedModule 44 · Applied Complex AnalysisLaurent series and the residue theorem
Not startedModule 45 · Applied Complex AnalysisConformal mapping
Not startedModule 46 · Numerical MethodsSources of error and significant figures
Not startedModule 47 · Numerical MethodsError propagation and numerical stability
Not startedModule 48 · Numerical MethodsBracketing methods (bisection and regula falsi)
Not startedModule 49 · Numerical MethodsOpen methods (Newton–Raphson and secant)
Not startedModule 50 · Numerical MethodsGaussian and Gauss–Jordan elimination
Not startedModule 51 · Numerical MethodsLU decomposition
Not startedModule 52 · Numerical MethodsIterative methods (Jacobi and Gauss–Seidel)
Not startedModule 53 · Numerical MethodsPolynomial interpolation
Not startedModule 54 · Numerical MethodsLeast squares regression
Not startedModule 55 · Numerical MethodsNumerical differentiation
Not startedModule 56 · Numerical MethodsNumerical integration
Not startedModule 57 · Numerical MethodsEuler's and Heun's methods
Not startedModule 58 · Numerical MethodsThe fourth-order Runge–Kutta method