Course Details

Course Information Package

Course Unit TitleCALCULUS AND ANALYTIC GEOMETRY I
Course Unit CodeAMAT111
Course Unit DetailsBSc Automotive Engineering (Required Courses) - BSc Mechanical Engineering (Required Courses) - BSc Computer Engineering (Required Courses) - BSc Computer Science (Required Courses) - BSc Civil Engineering (Required Courses) - BSc Quantity Surveying (Required Courses) - BSc Electrical Engineering (Required Courses) -
Number of ECTS credits allocated5
Learning Outcomes of the course unitBy the end of the course, the students should be able to:
  1. Explain the notion of a function of a real variable, define the absolute value function, state and use its properties and sketch the graph of linear, quadratic, and absolute value functions.
  2. Solve inequalities with absolute values, quadratic inequalities by factorizing and considering the two linear terms, rational inequalities and illustrate a geometric interpretation of the above inequalities by sketching the graph of the corresponding function.
  3. Define, sketch the graph, and describe the properties of the exponential function, the logarithmic function and the basic trigonometric functions.
  4. Explain the notion of limits and continuity of functions, identify and verify limits and points of discontinuity from a graph.
  5. Describe the derivative as a limit of finite differences, find the derivative of specific categories of functions, state and apply the general rules of differentiation to calculate derivatives, use the first and second derivative of a function to find its local extrema , points of inflection, and regions in which it is increasing, decreasing, concaving upwards or downwards.
  6. Apply the knowledge of derivatives in the field of engineering and in optimization problems.
  7. Explain in broad terms the concept of the integral of a function of a real variable.
Mode of DeliveryFace-to-face
PrerequisitesNONECo-requisitesAMAT100
Recommended optional program componentsNONE
Course Contents

Linear and other Inequalities in one Variable. Absolute Values and their Properties.

Exponents, roots and their properties. The concept of the logarithm and its properties. Exponential and logarithmic equations.

Basic trigonometric functions and their graphs (sinx, cosx, tanx, cotx, secx, cscx) and basic identities of trigonometric functions including trigonometric functions of sums and differences of two angles. 

Real valued functions of one variable: functions, operations of functions, inverse functions, logarithmic and exponential functions and their properties, parametric equations. Graphs of linear, quadratic, cubic, square root, exponential and logarithmic functions.

Limits and continuity: introduction to calculus, limits, and continuity.

Differentiation: The derivative as a function, the derivative as a rate of change and as the slope of a graph, techniques of differentiation, chain rule, derivatives of trigonometric, exponential, and logarithmic functions, higher derivatives, implicit differentiation, and differentials.

Applications of differentiation: related rates, increase, decrease, and concavity, relative extrema, first and second derivative tests, curve sketching, absolute minimum and maximum values of functions, applied maximum and minimum value problems.

Introduction to the concept of integration.

Recommended and/or required reading:
Textbooks
  • Anton H, Bivens I, and Davis S: “Calculus”, 7th Edition, John Wiley & Sons, 2002.
References
  • C. Henry Edwards, David E. Penney, Calculus, Matrix Version, Pearson Education, 6th edition, August 2002.
  • James Stewart, Calculus: Concepts and Context, Thomson Learning, 3rd Bk & CD edition, November 1, 2004.
Planned learning activities and teaching methods

The taught part of course is delivered to the students by means of lectures and several examples are solved on the white board. Students are asked to work on their own during class hours on practice problems, and they are encouraged to ask questions.

Many additional exercises are given to students to work at home, and analytic solutions are provided. Students are encouraged to attend office hours for extra help.

Assessment methods and criteria
Tests40%
Final Exam60%
Language of instructionEnglish
Work placement(s)NO

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