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Learning outcomes
The students after the successful completion of the course will have acquired all the basic concepts of mathematics that are essential in the field of health sciences. In particular they will be able to:
• Solve linear and quadratic algebraic equations
• Comment on graphical representations of real functions of one variable
• Understand the concept of derivative
• Compute the derivatives of simple, composite and inverse functions
• Compute the limit of a function
• Find the extremes of real functions of one variable with the use of first and second derivative and apply them in real problems
• Understand the use of integral and its applications in health sciences
• Appropriately use concepts from Calculus in problems that arise in the field of health sciences
SYLLABUS
The course is designed for a set of 13 weeks of lectures. The topics that will be discussed are the following
Linear Algebra
- Matrices (definition, types and operations)
- Determinant (definition, properties)
- Linear systems (Cramer method, Gauss algorithm)
- Inverse Matrix (computation and use in systems of linear algebraic equations)
Real Functions of One Variable
- Elementary functions
- Limit of a function – Continuity
- Differential Calculus of Functions of one variable
- Definition, Differentiation Rules, Derivatives of Elementary Functions
- Mean Value Theorem, Derivative of a Function and Monotonicity, Derivative and Local Extremes, L’Hopital Rule
- Curved Functions, Inflection Points
- Integral Calculus of functions of one variable
- The fundamental theorem of calculus.
- Integration techniques (integration by factors, recursively, rational functions, variable change).
- Definite integral, Integral applications
- Improper integral