Teaching Concepts With Maple – Teaching Engineering, Teaching Calculus, Teaching Algebra

Featured: Constrained Optimization

Demonstration

A constrained optimization problem is solved numerically with the Optimization assistant, and analytically with the Lagrange multiplier method implemented in the Lagrange Multipliers task template, and with first principles.

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Other Featured Examples

Why did I create these examples? Read Dr. Lopez’s blog post where he discusses the role of Maple in teaching mathematical concepts.

Full Topic List

Differential Calculus Derivatives by Definition: Polynomials Evaluation of a Limit Implicit Differentiation Tangent and Normal Lines Derivative of Square Root by Definition Constrained Optimization: Largest Rectangle with Fixed Perimeter Constrained Optimization: Rectangle Under an Ellipse Graph f and its Derivatives Related Rates: Two Ships Problem Rational Function Related Rates: Volume and Surface Area of a Sphere Taylor Polynomials Cubic with Prescribed Extrema Minimization Problem: Distance from a Point to a Curve Newton's Method Approximation by Differential Mean Value Theorem	Integral Calculus Riemann Sums Area between Curves Antidifferentiation as Area under a Curve Methods of Integration: Integration by Parts Definite Integration by Definition Volume of a Solid of Revolution: Rotation about x = 2 Work Conical Tank Numeric Integration: Trapezoid Rule Trig Substitution Sequence of Constants Trig Substitution Partial Sums for a Series of Constants Integration by Partial Fractions Volume by Slicing	Multivariate Calculus Level Curves and Plane Sections Tangent Plane Line Determined by Two Points Find and Classify Critical Points Skew Lines Gradient Vector Distance from a Point to a Line Directional Derivative Constrained Optimization Volume between Two Surfaces Center of Mass Surface Area
Differential Equations Direction Field Nullclines and Isoclines Picard Iteration Initial Value Problem Classification of an ODE First-Order Linear System of ODEs Lotka-Volterra Predator-Prey Model Nonlinear Autonomous System: Equilibrium Points and Phase Portrait	Linear Algebra Gaussian Elimination Vector Projection Projection onto a Plane Basis from a Set of Vectors Coordinates with Respect to a Basis Eigenvalues and Singular Values Eigenvalues and Eigenvectors Least-Squares Curve Fitting Generalized Eigenvalue Problem	Vector Calculus Frenet-Serret Formalism for a Helix Work or Circulation for a Vector Field Surface Flux for a Vector Field Evolute of a Plane Curve Integral Equivalence of Divergence Green's Second Identity Obtain the Directional Derivative Finding a Scalar Potential Finding a Vector Potential
Algebra and Precalculus Linear Equation in one Variable Linear Equations in two Variables Solving a Quadratic Equation Parameter Dependence of the Zeros of a Polynomial Intersecting Parabolas Analyze a Quadratic Relation Piecewise-Defined Functions Curve Defined Parametrically	Trigonometry Quadratic Trig Equation Quadratic Trig Equation with Different Functions Linear Trig Equation Made Quadratic to Solve Is It a Trig Identity? Principal Branch of a Trig Function Transforming Trig Functions