MATH 203 • Midterm • 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

Extreme Values

Exam like Question 1

Exam like Question 2

Exam like Question 3

Exam like Question 4

Extreme Values on Closed Regions 1

Extreme Values on Closed Regions 2

Exam like Question 1

Exam like Question 2

Exam like Question 3

Taylor Polynomials of Functions of Two Variables

Exam Like Question

Spring 2024 Midterm Exam Problem

Spring 2020 Exam: Cross Product Applications

Spring 2020 Exam: Cross Product Applications

Spring 2021 Exam: Cross Product & Dot Product

Spring 2019: Cross Product & Dot Product

Spring 2019: Vectors & Plane Equations

Spring 2023 : Plane Equations

Spring 2020 : Plane Equations

Spring 2020 : Intersection of Planes

Spring 2021 : Intersection of Planes

Spring 2022 Final Exam : Intersection of Planes

Spring 2020: Planes and Lines Equations

Fall 2020 : Planes and Lines Equations

Spring 2020: Intersection of Planes and Lines

Spring 2019: Intersection of Planes and Lines

Spring 2021 : Planes and Lines Equations

Spring 2022 : Planes and Lines Equations

Spring 2023: Vector Functions & Length of a Curve

Spring 2019: Vector Functions & Length of a Curve

Spring 2019: Vector Functions & Tangent Line

Spring 2022 : Unit Tangent, Curvature, Binormal

Spring 2016: Unit Tangent, Curvature, Binormal

Spring 2020: Curvature & Unit Tangent

Spring 2021: Vector Functions: Curvature

Spring 2021: Vector Functions: Torsion

Spring 2023: Limits of Multivariable Functions

Spring 2019: Limits of Multivariable Functions

Spring 2022 Final: Limits of Multivariable Functions

Spring 2020: The Chain Rule

Spring 2019: The Chain Rule

Spring 2023: The Chain Rule

Spring 2023: Gradient and Tangent Plane

Spring 2019: Gradient and Tangent Plane

Spring 2021: Gradient ,Tangent Plane and Normal Lines

Spring 2022: Tangent Plane & Approximation

Spring 2020: Tangent Plane & Approximation

Spring 2023: Gradient and Directional Derivative

Spring 2022 : Extreme Values

Spring 2023: Extreme Values on Restricted Region

Spring 2022 : Lagrange Multipliers

Applications of Cross Product

Intersection of Lines & Distance

Tangent Plane & Approximation

Gradient & Tangent Plane

Gradient & Partial Derivative

Applications of Cross Product

Distance between Planes and Lines

Planes and Lines

Vector Functions: Unit Tangent, Curvature

Vector Functions: Tangent Line

Extreme Values

Tangent Plane & Gradient

Directional Derivative & Gradient

Directional Derivative & Gradient

Directional Derivative & Gradient

Partial Derivative

Lagrange Multipliers

Extreme Values

Extreme Values

Extreme Values

Extreme Values on Closed Region 1

Extreme Values on Closed Region 2

Extreme Values on Closed Region 3

Vector Functions : Tangent Line

Vector Functions : Unit Tangent, Curvature, Length

Vector Functions : Curvature

Vector Functions: Unit Tangent & Curvature

Vector Functions: Unit Tangent & Curvature

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

Limit of Multivariable Functions 7

Continuity

Tangent Plane 1

Tangent Plane 2

Tangent Plane and Normal Line 1

Tangent Plane and Normal Line 2

Approximation 1

Approximation 2

Gradient & Tangent Plane

Directional Derivatives

Gradient & Directional Derivative

Gradient & Directional Derivative

Gradient & Directional Derivative

Gradient & Directional Derivative

Gradient & Directional Derivative

Gradient & Directional Derivative

Gradient & Directional Derivative

The Chain Rule 1

The Chain Rule 2

The Chain Rule 3

The Chain Rule 4

The Chain Rule 5

The Chain Rule 6

The Chain Rule 7

The Chain Rule 8

The Chain Rule 9

Chain rule and Tangent Plane

Chain Rule & Approximation