School Programmes, Syllabi & Academic Information.

MATHEMATICS for ENGINEERING

MATHEMATICS for ENGINEERING (81 hours)

Course Description: This course caters for students with a good background in mathematics, who are competent in a range of analytical and technical skills. The majority of these students will be expecting to include mathematics as a major component of their university studies, either as a subject in its own right or within courses such as physics, engineering and technology.

Aim of the Course: The course focuses on developing important mathematical concepts in a comprehensible, coherent and rigorous way. This is achieved by means of a carefully balanced approach. Students are encouraged to apply their mathematical knowledge to solve problems set in a variety of meaningful contexts. Development of each topic should feature justification and proof of results. Students embarking on this course should expect to develop insight into mathematical form and structure, and should be intellectually equipped to appreciate the links between concepts in different topic areas. 

Learning Outcomes:

  1. Knowledge and understanding: recall, select and use their knowledge of mathematical facts, concepts and techniques in a variety of familiar and unfamiliar contexts.
  2. Problem-solving: recall, select and use their knowledge of mathematical skills, results and models in both real and abstract contexts to solve problems.
  3. Communication and interpretation: transform common realistic contexts into mathematics; comment on the context; sketch or draw mathematical diagrams, graphs or constructions on both paper and using technology; record methods, solutions and conclusions using standardised notation.
  4. Technology: use technology, accurately, appropriately and efficiently both to explore new ideas and to solve problems.
  5. Reasoning: construct mathematical arguments through use of precise statements, logical deduction and inference, and by the manipulation of mathematical expressions.

Syllabus

Functions: Fundamental Definitions and Notions. Composite Functions. Sign Diagrams. Inequalities (In-equations): Solution with Sign Diagram. Asymptotes: Vertical Asymptote, Horizontal Asymptote, Oblique Asymptote, Inverse Functions: Identity Function, Inverse Function Definition, Fundamental Notions.

Sequences of Numbers: Arithmetic Sequences, Geometric Sequences, Series: Sum of Series, Sum of an Infinite Geometric Series.

Exponential Equations, Exponential-Logarithmic Functions, Exponential-Logarithmic Equations, Growth and Decay.

Graphing and Transforming Functions, Solving Quadratic Equations, Applications of Quadratics.

Radian Measure, Basic Trigonometric Functions, Mensuration, the Cosine Rule and the Sine Rule, Trigonometric Equations and Identities.

Geometry: Vectors Cartesian Co-ordinates, 2-D and 3-D Coordinate Geometry, Vector Algebra, The Scalar and Vector Products of Vectors. Straight Line Equations, Equations of Hyperbolas and Parabolas.

Linear Algebra: Vector spaces, Matrices and Matrix Algebra, Matrix Multiplication: Properties, Non Commutative Nature of Matrix Multiplication, the Distributive Law. Multiplicative Inverse of a Matrix: Invertible Matrices, Singular Matrices, Determinants. Solving A Pair Of Linear Equations: Solution Method, Geometric interpretation. Solving Systems of Linear Equations: Square Systems of Linear Equations, General Linear Systems.

Calculus: Limits, Informal Definition Of, Rules For Limits, Limits At Infinity. Finding Asymptotes Using Limits, Calculation of Areas under Curves: Upper Sums, Lower Sums, introducing the Definite Integral. The Derivative Function: The Slope of a Tangent, Secant, Calculating Derivatives from First Principles, The Derivative Function, Derivative Notations. Simple Rules of Differentiation, The Chain Rule: Derivatives of Composite functions. Product and Quotient Rules. Tangents and Normals. Higher Derivatives. Time Rate of Change and General Rates of Change. Motion In a Straight Line: Curve Properties and Sketching, Further Topics on Differentiation: Derivatives of other Families of Functions. Integration: Antidifferentiation and Antiderivative, The Fundamental Theorem of Calculus, Rules for Integration, Integration by Substitution, Integration by Parts, The Definite Integral and Areas, Finding Areas Between Curves, Applications To Motion Problems, Volumes of Revolution, Mean Values, Problem Solving by Integration.

Complex Numbers

Differential Equations: First Order, Separable, Integrating Factor, Second order With Constant coefficients. Numerical Methods.

Recommended Texts

  1. Mathematics for the IB Diploma: Higher Level with CD-ROM, Paul Fannon
  2. IB Mathematics Higher Level: For Exams from May 2014, Ian Lucas
  3. IB Mathematics Higher Level Course Book: Oxford IB Diploma Programme: For the IB Diploma, Josip Harcet
  4. Cambridge International AS&A Level Mathematics Pure Mathematics 1 by Sophie Goldie