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




Teaching Concepts with Maple is a collection of video examples and Maple documents that illustrates the re-sequencing of traditional concepts and skills that comes when students have access to a syntax-free, clickable tool such as Maple. Developed by Dr. Robert Lopez, each example shows how a problem can expeditiously be solved with a few clicks in Maple. Then, like peeling away the layers of an onion, various facets of the solution process are explored. From a big-picture conceptual approach, to a mastery of details, Maple helps the student learn more quickly, and with greater insight and understanding.



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List of Problems



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
Related-Rates Problem for a Scalene Triangle
Related Rates - The "Sand-Pile" Problem
Antiderivatives
Maximum and Minimum Curvature of an Ellipse
Minimize Area of a Triangle
Related Rates - A Sliding Ladder Problem
Related Rates - A Shadow Problem
Roots of a Polynomial and Its Derivative
Roots of a Polynomial and Its Second Derivative
Roots in Geometric Progression
Rational Function Satisfying Prescribed Conditions
Tangent to the Astroid
Parametrizing a Curve
One-Parameter Family of Quadratics

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
Separable ODE
Newton's Law of Cooling
Logistic Growth
Average Value
Mean Value Theorem for Integrals
Arc Length
Surface Area of Surface of Revolution
Volume of Revolution 1
Volume of Revolution 2
Volume of Revolution 3
Work Done Stretching a Spring
Work Done Winding a Cable
Work Done Stretching Spring of Unknown Length
Work Pumping a Cylindrical Tank
Hydrostatic Force on a Trapezoidal Dam
Hydrostatic Force on a Disk
Centroid of a Plane Region
Arclength of A Catenary
Numeric Integration - Simpson's Rule
Basic Identities for Hyperbolic Functions
Log Form of the Inverse Hyperbolic sine
Ratio Test for Series of Positive Constants
Series of Positive Constants
Convergence of a Power Series
Radius of Convergence of a Power Series
Taylor Series for sin(x)
Volume by Slicing 1
Volume by Slicing 2

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
Plane through Three Points
Constrained Optimization
Plane from Point and Normal
Volume between Two Surfaces
Plane Containing a Direction and Two Points
Riemann Sum for Iterated Double Integral
Center of Mass
Plane Orthogonal to Two Given Planes
Surface Area
Plane Containing a Given Point and the Line of Intersection of Two Planes
Average Value of a Function of Several Variables
Distance from a Point to a Plane
Distance between Parallel Planes
Line from Point to Line and Parallel to Plane
Lines in a Plane Equidistant from a Point
Line Parallel to Two Planes and on Two Lines
Line at a Fixed Distance from Given Line
Line at Max or Min Distance from a Given Point
Plane at Max Distance from Given Point
Plane Making Prescribed Angles with Other Planes
Orthocenter of First-Octant Triangle
Line with Prescribed Length
Jacobian of a Transformation
Volume inside a Triangular Cylinder

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
Simultaneous Diagonalization

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
Inverse Functions
Induction
Binomial Theorem
Arithmetic Sequence
Geometric Sequence
Partial Sums of a Geometric Series
Recursively-Defined Sequence

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

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