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

Graphs of Surfaces

Exam like Question 1

Exam like Question 2

Exam like Question 3

Exam like Question 4

Parametric Equations 1

Parametric Equations 2

Exam like Question 1

Exam like Question 2

Exam like Question 3

Exam like Question 4

Exam like Question 5

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 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: Length of a Curve

Spring 2019: 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

Vectors: Cross Product & Dot Product

Vectors & Plane Equations

Planes and Lines Equations

Planes and Lines Equations

Limits of Multivariable Functions

Vector Functions: Length of a Curve

Vector Functions : Equation of a Tangent Line

The Chain Rule

Gradient and Tangent Plane

Cross Product : Area of Triangles

Cross Product : Volume of Paralellopiped

Plane Equations

Intersection of Planes

Plane and Lines Equations

Planes and Lines Equations

Curvature & Unit Tangent

The Chain Rule

Directional Derivative and Tangent Plane

Cross Product & Dot Product

Planes and Lines Equations

Vector Functions: Curvature

Vector Functions: Torsion

Gradient , Tangent Plane and Normal Lines

Spring 2022 Final Exam : Planes and Lines

Spring 2022 Midterm : Planes and Lines

Spring 2022 Midterm : Unit Tangent, Curvature, Binormal

Spring 2022 Final: Limits of Multivariable Functions

Spring 2022: Tangent Plane & Approximation

Spring 2022 : Extreme Values

Spring 2022 : Lagrange Multipliers

Plane Equation

Vector Functions: Length of a Curve

Limits of Multivariable Functions

Gradient and Tangent Plane

Gradient and Directional Derivative

The Chain Rule

Extreme Values on Restricted Region

Lagrange Multipliers

Cross Product & Dot Product

Plane Equations & Intersection

Limits of Multivariable Functions

Continuity of Multivariable Functions

Vector Functions

Gradient & Tangent Plane

Higher Order & Directional Derivative

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

Lines & Planes & Vectors in Space

Vector Functions & Unit Tangent , Binormal

Linear Approximation & Gradient

Equation of a Tangent Plane

Extreme Values on Closed Region

Vector Functions : Unit Tangent, Curvature, Length

Arc Length

Arc Length

Arc Length

Arc Length

Vector Functions : Curvature

Vector Functions: Unit Tangent & Curvature

Space Curves & Vector Functions 1

Vector Functions: Unit Tangent & Curvature

Domain of Multivariable Functions

Domain of Multivariable Functions

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

Limit of Multivariable Functions 8

Continuity

Vectors & Dot and Cross Product

Equation of Planes

Equation of Planes

Plane and Lines

Plane and Lines

Plane and Lines

Distance between Planes and a Point

Distance between Planes and Lines

Distance between Lines and a Point