Learning Mathematics
using Maple

Mathematics for Introductory Science Courses:

• Vectors 1: Cartesian Coordinates  📄 (PDF)

• Vectors 2: Vector Products  📄 (PDF)
  
  

• Calculus 1: Limits & Differentiation  📄 (PDF)

• Calculus 2: Integration  📄 (PDF)

  • Calculus 2D: Integration - Data 📄 (PDF)

  • Calculus 2N: Integration - Numeric Integration - Monte Carlo 📄 (PDF)

    • Calculus 2Nx: A Response to Prof. Lopez's Video 📄 (PDF)

• Calculus 3: Summations & Series  📄 (PDF)
  📄 Exercises      📄 Solutions - Limits, Derivatives   📄   Solutions - Integrals, Summations, Series
  
  

• Complex Numbers 1: Fundamentals  📄 (PDF)

• Complex Numbers 2: Fractional Powers  📄 (PDF)
  📄 Exercises   📄  Solutions
  
  

• Statistics 1: Descriptive Statistics 📄 (PDF)

• Statistics 2: Curve Fitting: Linear and Non-Linear Curves 📄 (PDF)

• Statistics 3: Curve Fitting: Polynomial Interpolation and Spline Fit 📄 (PDF)

Advanced Mathematics for Undergraduates:

• Ordinary Differential Equations 1: Symbolic  📄 (PDF)

• Ordinary Differential Equations 2: Numeric  📄 (PDF)

  • Ordinary Differential Equations 2: Numeric - Parameterized Solutions 📄 (PDF)

  • Ordinary Differential Equations 2: Numeric - Animate and Explore 📄 (PDF)

• Ordinary Differential Equations 3: Systems of ODEs  📄 (PDF)

• Ordinary Differential Equations: Boundary Value Problems 📄 (PDF)

• Linear Algebra 1: Matrices & Matrix Arithmetic  📄 (PDF)

• Linear Algebra 2: Eigenvalues & Eigenvectors  📄 (PDF)

• Linear Algebra 3: Linear Transformations  📄 (PDF)
  
  

• Partial Differential Equations 1: Solving Symbolic Equations (Part 1) (Part 2)   📄 (PDF)

• Partial Differential Equation Example: Heat Equation 📄 (PDF)

• Partial Differential Equation Example: Heat Equation in 2D 📄 (PDF)

• Partial Differential Equation Example: Wave Equation in 2D 📄 (PDF)
  
  

• Vector Calculus 1: Vectors & Vector Field 📄 (PDF)

• Vector Calculus 2: Differentiation 📄 (PDF)
  
  

• Advanced Mathematics: Fourier Series 📄 (PDF)

• Advanced Mathematics: Orthogonal Polynomial Functions 📄 Exercises    

• Advanced Mathematics: Transformations 📄 (document)

• Advanced Mathematics: Dirac delta function 📄 (document)

Applications:

• Stratospheric Jump: 1D ODEs solved numerically 📄 (PDF)

• Baseball Trajectory: 2D ODEs solved numerically 📄 (PDF)

• Geometric Eigenvalues: Eigenvalue problem 📄 (PDF) 🍁(worksheet)

• Numerical Integration: Plotting a function of a triple integral 📄 (PDF) 
  🎥 (full worksheet development video)

• Double Pendulum: 2D ODEs in polar coordinates 📄 (document) 🍁(worksheet)