INTRODUCTION TO THE COURSE
INTRODUCTION TO MATHEMATICS Subject Code: DM015 (Semester 1) DM025 (Semester 2) Code Interpretation: DM = Mathematics for Science students (4 semesters programme) 01 / 02 = Semester 1 / Semester 2 5 = 5 credit units (5 hours T&L)
SYLLABUS
MATHEMATICS (SCIENCE) DM015 • 1.1 INDICES • Define, state, apply and solve equation • 1.2 SURDS • Define, express surd in simplified form • Algebraic operation and solve equations • 1.3 LOGARITHMS • Define, state law , change the base and solve equation. CHAPTER1 INDICES, SURDS AND LOGARITHMS • 2.1 LINEAR EQUATIONS • Define and solve simultaneous equations • 2.2 QUADRATIC EQUATIONS • Define, solve, type of root and solve simultaneous equations • 2.3 CUBIC EQUATIONS • Define and solve equation. CHAPTER 2 EQUATIONS
• 3.1 INEQUALITIES • Understand basic concept and use the properties. • Solve linear and quadratic inequalities • Solve simple rational inequalities. • 3.1 ABSOLUTE VALUES • Define, state and use properties, • Solve linear and absolute values linear inequalities. CHAPTER 3 INEQUALITIES AND ABSOLUTE VALUES •4.1 RELATIONS AND FUNCTIONS •Concept of relation and define domain and range. •4.2 TYPE OF FUNCTIONS •Sketch graph linear, quadratic, cubic and surds •Domain and range of linear, quadratic, cubic and surd. •4.3 COMPOSITE FUNCTION •Represent using arrow diagram and composite of two functions. •4.4 INERSE FUNCTION •Show function has an inverse and find the inverse •Compute inverse of function. CHAPTER 4 FUNCTIONS MATHEMATICS (SCIENCE) DM015
MATHEMATICS (SCIENCE) DM015 • 5.1 ANGLES AND THEIR MEASURES • Define angle and measures in degrees and radians and show positive and negative angles. • 5.2 TRIGONOMETRIC FUNCTIONS • Determine trigonometric function for some special angles and solve basic trigonometric equations. • 5.3 TRIGONOMETRIC IDENTITIES • 5.4 TRIGONOMETRIC FORMULAE CHAPTER 5 TRIGONOMETRIC • 6.1 ARITHMETIC SERIES • Identify, determine nth term and sum formula of arithmetic • 6.2 GEOMETRIC SERIES • Identify, determine nth term and sum formula of geometric • APPLICATIONS OF ARITHMETIC AND GEOMETRIC SERIES • Solve problem CHAPTER 6 ARITHMETIC SERIES AND GEOMETRIC SERIES
• 7.1 MATRICES • Identify different type, transpose matrix and perform operations on matrices. • 7.2 DETERMINANT OF MATRICES • Minor ,cofactors and determinant of matrix • 7.3 INVERSE OF MATRICES • Find inverse • 7.4 SYSTEM OF LINEAR EQUATION WITH THREE VARIABLES • Solve the unique solution by using inverse matrix. CHAPTER 7 MATRICES • 8.1 CIRCLES • Define circle • Determine the equation of a circle with radius r and center (h,k) • Determine the center and radius by using completing the square • Determine the equations of circle passes through three points. CHAPTER 8 CIRCLES MATHEMATICS (SCIENCE) DM015
• 1.1 LIMITS • State limit of function • Basic properties • One sided limits • Existence of the limit CHAPTER 1 LIMITS • 2.1 DERIVATIVE OF A FUNCTION • Relate the concept to the gradient and find derivate using first principles. • 2.2 TECHNIQUES OF DIFFERENTIATION • Basic properties, sum product, quotient rules and chain rule. • Derivative of combination of the functions • Second derivative CHAPTER 2 DIFFERENTIATION MATHEMATICS (SCIENCE) DM025
• 3.1 DIFFERENTIATION OF EXPONENTIAL FUNCTIONS. • 3.2 DIFFERENTIATION OF LOGARITHMIC FUNCTIONS • 3.3 DIFFERENTIATION OF TRIGONOMETRIC FUNCTIONS. • 3.4 DIFFERENTIATE FUNCTIONS INVOLVING TRIGONOMETRIC, EXPONENTIAL AND LOGARITHMIC FUNCTIONS. CHAPTER 3 DIFFERENTIATION OF EXPONENTIAL, LOGARITHMIC AND TRIGONOMETRIC FUNCTIONS. • 4.1 GRADIENT, TANGENT AND NORMAL TO A CURVE • Find gradient, equation of tangent and normal to a curve. • 4.2 CURVE SKETCHING • Stationary point, minimum and maximum points by using the first and second derivative test. • Sketch the graphs • 4.3 OPTIMISATION PROBLEMS • 4.4 RATES OF CHANGE CHAPTER 4 APPLICATION OF DIFFERENTIATION MATHEMATICS (SCIENCE) DM025
•5.1 INTEGRATION OF FUNCTIONS •Define as antiderivative, use basic rule and evaluate integral by substitution. •5.2 DEFINE INTEGRALS •Define definite integral for continuous function and determine the value of the definite integral. CHAPTER 5 INTEGRATION •6.1 INTEGRATION OF EXPONENTIAL FUNCTIONS •6.2 INTEGRATION OF LOGARITHMIC FUNCTIONS •6.3 INTEGRATION OF TRIGONOMETRIC FUNCTIONS •6.4 INTEGRATION BY PARTS CHAPTER 6 INTEGRATION OF EXPONENTIAL, LOGARITHMIC AND TRIGONOMETRIC FUNCTIONS. MATHEMATICS (SCIENCE) DM025
• 7.1 AREA OF THE REGION • 7.2 VOLUME OF THE REGION CHAPTER 7 APPLICATION OF INTEGRATION MATHEMATICS (SCIENCE) DM025