Math 126 Problems Page
Math 126 Problems Page
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Pre-Midterm 1
Section 1.1: Introduction and Review
Section 1.2: Coordinates
Section 2.1: Vectors: Geometry
Section 2.2: Vectors: Components
Section 3.1: Dot Products
Section 3.2: Dot Products: angles
Section 3.3: Dot Products: lengths and projections
Section 3.4: Dot Products: wrap up
Section 4.1: Cross Products: mechanics
Section 4.2: Cross Products: geometry
Section 5.1: Lines and Planes: introduction
Section 5.2: Lines and Planes: doing it!
Section 6: Surfaces
Section 7.1: Vector valued functions: theory
Section 7.2: Vector valued functions: practice
Section 8.1: Vector calculus: derivatives
Section 8.2: Vector derivatives in practice
Section 8.3: Vector integrals
Section 9: Polar Coordinates
Section 10.1: Distance
Section 10.2: Arc Length
Section 10.3: Curvature
Practice Midterm 1's
Pre-Midterm 2
Section 11: Tangents, Normals, and Binormals
Section 12: Tangential and Normal acceleration
Section 13: Multivariable Functions
Section 14.1: Partial derivatives
Section 14.2: Tangent planes
Section 15.1: Differentials
Section 15.2: Optimization
Section 16.1: Local max/min: theory
Section 16.2: Local max/min: examples
Section 17.1: Double integrals: Riemann sums
Section 17.2: Double integrals: first examples
Section 17.3: Double integrals: iterated integrals
Section 18: Double integrals over regions
Section 19: Double integrals in polar coordinates
Section 20.1: Area
Section 20.2: Center of mass
Practice Midterm 2's
Pre-Final Exam
Section 21: Errors in linear approximation
Section 22: Higher order approximation, Taylor Polynomials
Section 23: Even higher order approximation
Section 24: Making new Taylor series from old ones
Section 25: Taylor Summary
Practice Finals
Contact
Section 3.1: Vectors: Dot Product Mechanics
Compute the dot product of the following vectors:
$\langle1,2,3 \rangle \cdot \langle 3,2,1 \rangle$
$\langle 1,0,0 \rangle \cdot \langle 0, 1, 0 \rangle$
$\langle 1,0,\cdots,0\rangle \cdot \langle 0, \cdots, 0, 1 \rangle$
Solution