Chapter I: VECTORS IN R2
Mon
Wed
Thu
Feb13
Feb15
Feb16
Feb20
Feb22
Feb23
Feb27
Mar01
Mar02
Mar06
Mar08
Mar09
1.1. Vectors in R2: Basic definitions. The vector and
the scalar. Algebra of vectors. Properties of vectors. The
magnitude of a vector and its properties. The unit vector in
the direction of another vector.
1.2. The Dot Product: Definition and properties of
the dot product.
1.3. The Projection of a Vector upon another:
1.4. The Angle between Two Vectors: Basic
definitions and conventions. Finding the angle between
two vectors. Orthogonal vectors.
1.5. Geometric Representation: The triangle
(parallelogram) law.
Chapter II: VECTORS IN R3
2.1. R3: The three dimensional coordinate system. The
right- hand coordinate system and coordinate axes. The
coordinate planes. The ordered triple. The coordinate of a
point in R3. The coordinates of points in the coordinate
planes and the coordinates of points on the axes. Te
projection of a point into a coordinate plane. The distance
between two points. The equation of a sphere. The
midpoint on a line segment in R3.
2.2. Comparing R, R2 and R3: Points and sets in the
three systems. The interpretations of equations and
inequalities in the three systems. The concepts of a region
and a surface.
2.3. Vectors in R3:
2.3.1. Vectors in R3: Basic definitions. The vector and
the scalar. Algebra of vectors. Properties of vectors. The
magnitude of a vector and its properties. The unit vector in
1
the direction of a given vector.
Mar13
Mar15
Mar16
Mar20
Mar22
Exam1
Mar23
2.3.2. The Dot Product: Definition and properties of the
dot product.
2.3.3. The Projection of a Vector upon another
2.3.4. The Angle between Two Vectors: Basic
definitions and conventions. Finding the angle between
two vectors. Orthogonal vectors.
2.4. Direction Numbers: The set of direction angles
and the set of direction cosines for a vector. Sets of
direction numbers for a vector.
2.5. Straight Lines In R3: The two sets of direction
angles and the two sets of direction cosines for a straight
line. Sets of direction numbers for a straight line. Parallel
and perpendicular lines. Parametric representations for a
straight line. Symmetric equations for a straight line.
2.6. Cross Product: Properties of the cross product.
2.7. The Plane: The general equation of the plane.
Parallel and perpendicular planes. A normal to a plane.
2.8. Cylindrical And Spherical Coordinates:
Cylindrical and spherical representations of a point.
Transforming equations from rectangular coordinates to
cylindrical and spherical coordinate and visa versa.
First Examination: Mar 22
2
Mar27
Mar29
Mar30
Apr03
Apr05
Apr06
Apr10
Apr12
Apr13
Apr17
Apr19
Apr20
Apr24
Apr26
Apr27
May01
May03
Exam2
May04
Chapter IV: FUNCTIONS OF
SEVERAL VARIABLES
4.1.1. Basic Concepts: The domain of a function of
two variables. Algebra of functions of two variables.
4.1.2. Level Curves
4.2. Limit of a Function of Two Variables:
Equivalent definitions of a function of two variables.
Algebra of limits.
4.3. Continuity of a Function of Two
Variables: The domain of a function of two variables.
Algebra of functions of several variables.
4.4. Partial Derivatives: Rules for partial
differentiation. Clairout’s Theorem. Geometric
Interpretation.
4.5. The Differential: Differentiability of a function
of two variables.
4.6. The Chain Rule
4.7. Directional Derivatives: The gradient. The
directional derivative.
4.8. Tangent Planes
4.9. Extrema: Local maximum and minimum.
Absolute extremun. Boundary extremum. Test for local
extrema.
4.10. Constrained Extrema: Lagrange’s theorem.
Lagrange’s multipliers and theorem for a function
constrained by more than one condition.
Second Examination: May 3
3
May08
May10
May11
May15
May17
May18
Chapter V: MULTIPLE INTEGRALS
5.1. Iterated Integrals
5.2. Double Integral: Definition and properties of
double integral. Using symmetry to evaluate some double
integrals.
5.3. Double integral in Polar Coordinates
5.4. Triple Integral: Definition and properties of
triple integral.
5.5. Triple integral in Cylindrical Coordinates
5.6. Triple integral in Spherical Coordinates
4
Page 5
Evaluation
 First Examination:
17%
 Second Examination:
17%
 Quizzes:
10%
 Final Examination:
40%
 Project:
10%
 Assignments
06%
Office Hours
 Sunday & Wednesday: Lecture 4 : 11.00 - 12.00
5