Quiz and Midterm Review: The number before each definition or theorem indicates the number of the quiz for which you must memorize the item. On the midterm, you are responsible for all definitions and theorems up to that point.

Definitions: Memorize the following definitions. You may use either the definition given in class or the one in the book. Generally these will be the same, anyway. For any definition indicated with a *, be prepared to explain the definition with a diagram and a short essay. Pretend you are writing a section for a textbook on the definition.

Quiz 1) R^2 and R^3
Quiz 1) Vector addition (p. 798) *
Quiz 1) Scalar multiplication (p. 799) *
Quiz 1) Standard basis vectors (p. 802-803)
Quiz 1) Resultant force (p. 804)

Quiz 2) Dot product (p. 807)
Quiz 2) Cross product (p. 814)
Quiz 2) Determinants of order 2 and 3 (p. 814)

Quiz 3) Angle between two planes (p. 827) *

Quiz 4) Parametric equations for a curve, parameter (p. 651)
Quiz 4) Initial and terminal points of a curve (p. 652)
Quiz 4) Vector valued function, component functions (p. 849)
Quiz 4) Limit of a vector valued function (p. 849)
Quiz 4) Continuous vector valued function (p. 850)
Quiz 4) Derivative of a vector valued function (p. 856-857)
Quiz 4) Smooth curve (p. 858) *
Quiz 4) Definite integral of a vector valued function (p. 860)

Midterm) Arclength formula (p. 862) *
Midterm) Arclength parametrization (p. 863)
Midterm) Curvature of a curve (p. 864) *
Midterm) Unit tangent vector (p. 864)
Midterm) Unit normal vector (p. 867)

Quiz 5) Function of two variables (p. 887)
Quiz 5) Graph of a function of two variables (p. 890)
Quiz 5) Level curves (p. 892) *
Quiz 5) Limit of a function of two variables (p. 902) *
Quiz 5) Continuous function of two variables (p. 906)
Quiz 5) Partial derivatives of a function of two variables (p. 911) *
Quiz 5) Differentiable function of two variables (p. 926)
Quiz 5) Tangent Plane (p. 923)

Quiz 6) Directional Derivative (p. 941) *
Quiz 6) The gradient of a function (p. 944)
Quiz 6) Local maximum or minimum of a function of two variables (p. 953)
Quiz 6) Stationary point of a function of two variables (p. 954)

Quiz 7) Double integral of a function over a rectangle (p. 983)
Quiz 7) Average value of a function over a region (p. 986)

Theorems: Memorize the statements of the following theorems. If the statement is marked with a *, be prepared to explain what it means in an essay and using a diagram. If it is marked with a %, memorize the proof of it.

Quiz 1) Distance formula in three dimensions (p. 795) %
Quiz 1) Equation of a sphere (p. 796)
Quiz 1) Formulas for vector addition and subtraction and scalar multiplication in terms of components (p. 801)
Quiz 1) Properties of vectors (p. 802)

Quiz 2) Properties of dot product (p. 807). Be able to prove distributivity (part 3)
Quiz 2) Law of cosines (Theorem 3, p. 808) %
Quiz 2) Orthogonality lemma (box 7, page 809)
Quiz 2) Component of b on a (scalar projection) and projection of b on a formulas (p. 811) *
Quiz 2) Geometric description of cross product (Theorems 5,6 p. 816, 2nd box page 817) *
Quiz 2) Parallel lemma (Corollary 7 p. 817)
Quiz 2) Properties of cross product (p. 818)
Quiz 2) Volume lemma (Box 11, p. 819) *

Quiz 3) Vector equation of a line parallel to a vector v and passing through a point P (p. 822) *
Quiz 3) Parametric equations for a line parallel to v and passing through P (p. 823)
Quiz 3) Symmetric equations for a line parallel to v and passing through P (p. 823)
Quiz 3) Vector equation for the plane with normal vector n and passing through P (p. 825) *
Quiz 3) Scalar equation of the plane with normal vector n and passing through P (p. 826)

Quiz 4) Geometric interpretation of the derivative of a vector valued function (p. 857) *
Quiz 4) The derivative of a vector valued function (Thm 2, p. 857)
Quiz 4) Differentiation rules for vector valued functions (p. 859). Be able to prove 4 %
Quiz 4) If r(t) parametrizes a path on a sphere centered around the origin, then its tangent vector is perpendicular to its position vector for all t. %
Quiz 4) The Fundamental Theorem of Calculus for vector valued functions (p. 860)

Midterm) Alternative formula for curvature (#9 p. 864) %
Midterm) Velocity = derivative of position (class notes)%
Midterm) Components of acceleration (p. 874) *, %

Quiz 5) Clairaut's Theorem (p. 916)
Quiz 5) Differentiability theorem (8, p. 926)
Quiz 5) Chain Rule, case 1 (p. 932)
Quiz 5) Chain Rule, case 2 (p. 933)
Quiz 5) General Chain Rule (p. 934)
Quiz 5) Implicit function theorem (6, p. 936)

Quiz 6) Directional derivative theorem (3, p. 942) %
Quiz 6) Geometric interpretation of the gradient (15, p. 946)%
Quiz 6) The gradient of f(x,y) is perpendicular to its level curves or surfaces (p. 947) %
Quiz 6) First derivative test for local extrema (2, p. 953)
Quiz 6) Second derivative test for local extrema (3 p. 954)
Quiz 6) Extreme value theorem for functions of two variables (8, p. 959)

Quiz 7) Method of Lagrange Multipliers (p. 966) % (in case of two variables)
Quiz 7) Method of Lagrange Multipliers for two constraints (p. 969)
Quiz 7) Fubini's Theorem