MTE 203 - Advanced Calculus

MTE 203

Lecture 1: Introduction to Multivariable Functions and Surfaces

• 3D Cartesian Space
  • Octants
• Surfaces
• Level Curves and Contour Plots

Lecture 2: Vectors and Vector Valued Functions

• Vector Review
  • Dot Product
  • Cross Product
• Vector Functions
• Vector Equations of Lines
• Vector Equations of Planes

Lecture 3: Differentiation and Integration of Vector-valued Functions and the Parametrization of Curves

• Limits of Vector Functions
• Derivatives of Vector Functions
• Integration of Vector Functions
• Parametrizing Curves

Lecture 4: Tangent vectors, arc length and unit tangent vectors

• Tangent Vector
• Smooth Curves
• Arc Length

Lecture 5: Normal Vectors, Curvature, and Radius of curvature

• Normal Vectors
• Binormal Vector
• Curvature, Radius of Curvature, Circle of Curvature
• Radius of Curvature

Lecture 6: Multivariable functions, Limits and Continuity

• Multivariable Functions
• 2D Limits
• Continuity for 2D Functions

Lecture 7: Partial Derivatives and Gradient Vector

• Partial Derivatives
• Gradient Vector

Lecture 8: Higher Order Partial Derivatives and Chain Rule

• Higher Order Partial Derivatives
• Laplace’s Equation
• Chain Rule for Partial Derivatives

Lecture 9: Implicit Differentiation

• Implicit Differentiation with Partial Derivatives
• Jacobian Determinate

Lecture 10: Directional derivatives, tangent lines, and tangent plane

• Directional Derivatives
• Tangent Lines and Planes

Lecture 11: Optimization 1

• Critical Point
• Relative Extrema
• Saddle Point
• Critical Point Test

Lecture 12: Optimization 2

• Absolute Extrema

Lecture 13: Lagrange Multipliers

• Lagrange Multipliers

Lecture 14: Applications

• Least Squares
• Differentials

Lecture 15: Double Integration

• Double Integration

Lecture 16: Double Integration and Triple Integration

• Triple Integration

Lecture 17: Double Integrals with Polar Coordinates

• Double Integrals with Polar Coordinates

Lecture 18: Triple Integrals in Cylindrical and Spherical Coordinates

• Triple Integrals in General Coordinates

Lecture 19: Center of Mass and Moments of Inertia

• Center of Mass and Moments of Inertia

Lecture 20: Areas and volumes of rotation

• Areas and volumes of rotation

Problems

• Suggested Problems
• MATLAB Worksheet 1
• MATLAB Worksheet 2
• Project 1 - Robot Kinematics
• Project 2 - Recurrent Neural Networks