TENTATIVE SYLLABUS for first nine weeks
Exponents and logarithms first 2 weeks
▪ Change of base
▪ Laws of Exponents; laws of logarithms
▪ Graph exponential and logarithmic functions
▪ Solve both exponential and logarithmic functions.
Complex numbers next: 3 weeks
▪ real part, imaginary part, conjugate, modulus and argument
▪ Cartesian form z=a + ib (2-D vectors)
▪ Modulus-argument form (polar form)
▪ Sums, products and quotients of complex numbers
▪ De Moivre’s theorem
▪ Powers and roots of a complex number
▪ Conjugate roots of polynomial equations with real coefficients
Mathematical Induction: a week
▪ Proof by mathematical induction (Process of induction and principle od induction)
▪ Indirect proof
▪ Forming conjectures to be proved by mathematical induction
Vectors and planes, Solution of system of linear equations 5 weeks
Solution of Linear Equations
▪Unique solution
▪No solution
▪Infinity of solutions
▪Find solution(s), if any exist, of a set of linear equations using matrix techniques.
▪Write solution(s) as a point, line, or plane.
Vectors in Two and Three Dimensions
▪Graph vectors in 2 and 3 dimensions.
▪Represent vectors using vector notation.
Components of a Vector
▪Identify the components of a vector.
Addition and Multiplication of Vectors
▪Add vectors.
▪Multiply vectors by a scalar.
▪Graph the resultant vector.
Length of Vector
▪Calculate the length (magnitude) of a vector.
▪Write down the unit vector for a given vector.
Scalar Products and Projections
▪Calculate the scalar product.
▪Find the angle between 2 vectors using scalar product formula.
▪Prove orthogonality.
Vector Products
▪Calculate the vector product of 2 vectors.
▪Find a 3rd vector that is perpendicular to 2 other vectors.
Geometric Application of the Vector Product
▪Use of the formula involving vector product, magnitudes, and sine of the angle.
Algebra of Scalar and Vector Products .
▪Show that two vectors are orthogonal.
▪Use the formula magnitude of cross product equals the product of the squared magnitudes minus
the square of the dot product.
Lines and Planes
▪Express equations of lines and planes in parametric, cartesian, and normal form.
Intersections of:
▪Two lines
▪Line with a plane
▪Two planes
▪Three planes
Distances in Three Dimensions
▪Write expressions and calculate the distance between 2 objects (points, lines, or planes) in 3-d.