MATH 203 • Midterm I • Multivariable Calculus

Distance Between Points 1

Cosine Theorem in 3D & Euclidean N-Space

Vectors: Arithmetic, Parallelism and Unit Vector

Angles between Vectors : Dot Product

Vector Projection

Cross Product of Vectors

Applications of Cross Product

Plane Equations

Line Equations 1

Line Equations 2

Intersection of Planes

Intersection of Planes and Lines

Distance of a Point to Lines & Planes

Vector Functions and Curves

Domain of a Vector Function

Limit of a Vector Function

Derivative of a Vector Function

Integral of a Vector Function

Position, Velocity, Acceleration

Position, Velocity, Acceleration 2

Arc Length

Arc Length Parametrization

Tangent, Normal, Binormal Vectors and Curvature, Torsion

Calculation of Tangent, Normal, Binormal Vectors and Curvature, Torsion

Unit Tangent, Unit Normal, Binormal Vectors 1

Unit Tangent, Unit Normal, Binormal Vectors 2

Unit Tangent, Unit Normal, Binormal Vectors 3

Unit Tangent, Unit Normal, Binormal Vectors 4

Curvature 1

Curvature 2

Curvature 3

Curvature 4

Torsion 1

Torsion 2

Domain of Functions

Level Curves

Limits of Multivariable Functions 1

Limits of Multivariable Functions 2

Limits of Multivariable Functions 3

Continuity of Multivariable Functions

Exam like Question 1

Exam like Question 2

Limit Definition of Partial Derivative

Partial Differentiation Rules 1

Partial Differentiation Rules 2

Higher Order Partial Differentiation

Chain Rule 1

Chain Rule 2

Chain Rule 3

Equation of a Tangent Plane 1

Equation of a Tangent Plane 2

Horizontal Tangent Plane

Normal Vector to a Multivariable Function

Tangent Plane Approximation

Gradient Vector

Directional Derivative

Gradient and Directional Derivative

Implicit Differentiation I

Implicit Differentiation II

Implicit Differentiation III

Implicit Higher Differentiation

Cross Product Applications 1

Cross Product Applications 2

Cross Product Applications 3

Cross Product Applications 4

Planes Equations and Coplanarity

Planes Equations and Coplanarity 2

Intersection of Planes

Angle between Planes

Intersection of Lines

Angle between Lines

Plane and Lines 1

Planes and Lines 2

Plane and Lines 3

Planes and Lines 4

Planes and Lines 5

Distance of a Point to Lines & Planes I

Distance of a Point to Lines & Planes II

Distance of a Point to Lines & Planes III

Distance of a Point to Lines & Planes IV

Position Vectors 1 : Velocity,Speed,Acceleration

Position Vectors 2 : Velocity,Speed,Acceleration

Position Vectors 3 : Velocity,Speed,Acceleration

Position Vectors 4: Velocity, Speed, Acceleration

Parametric Equation for Tangent Line

Parameterization of the Curves 1

Parameterization of the Curves 2

Parameterization of the Curves 3

Parameterization of the Curves 4

Parameterization of the Curves 5

Position Vectors 5: Velocity, Speed, Acceleration

Position Vectors 6: Velocity, Speed, Acceleration

Length of the Curves 1

Length of the Curves 2

Length of the Curve 3

Length of the Curve 4

Length of the Curves 5

Length of the Curves 6

Limit of Multivariable Functions 1

Limit of Multivariable Functions 2

Limit of Multivariable Functions 3

Limit of Multivariable Functions 4

Limit of Multivariable Functions 5

Limit of Multivariable Functions 6

Continuity 1

Continuity 2

Definition of Partial Derivative 1

Definition of Partial Derivative 2

Definition of Partial Derivative 3

Tangent Plane 1

Tangent Plane 2

Tangent Plane 3

Tangent Plane and Normal Line 1

Tangent Plane and Normal Line 2

Approximation 1

Approximation 2

Gradient and Tangent Plane 1

Gradient and Tangent Plane 2

Gradient and Tangent Plane 3

Gradient and Directional Derivative 1

Gradient and Directional Derivative 2

Gradient and Directional Derivative 3

Gradient and Directional Derivative 4

Gradient and Directional Derivative 5

Gradient and Directional Derivative 6

Higher Order Derivative 1

Higher Order Derivative 2

Higher Order Derivative 3

Chain Rule 1

Chain Rule 2

Chain Rule 3

Chain Rule 4

Chain Rule 5

Chain Rule 6

Chain Rule and Tangent Plane

Chain Rule and Higher Order Derivative

Implicit Differentiation

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Bonus Problem

Planes

Lines

Tangent Plane

Gradient

Tangent Plane