Limits of Real-Valued Functions - Advanced Calculus (Undergraduate Advanced)

Limits dictate how mathematical models predict exact behaviour at critical points. This course covers formal and informal definitions of finite and infinite limits. You will study direct substitution, algebraic factorisation, conjugate multiplication, the squeeze theorem, and piecewise function analysis. The material handles indeterminate forms through derivative ratio techniques and rationalisation. Each method includes repeated worked examples to fix the procedure in your mind. Engineers and analysts use limit evaluation to calculate instantaneous speed, stress thresholds in structures, and signal decay rates. Financial planners apply these rules to compound interest and market trend forecasting. Computer simulation software relies on accurate limit logic to prevent calculation crashes and rounding errors. Mastery of this material gives you reliable tools for real technical modelling and removes guesswork from system analysis. You will construct formal proofs for finite and infinite limits using strict logical bounds. You will select the correct evaluation method from substitution, algebra, or derivative rules without hesitation. You will resolve indeterminate forms and apply boundary checks to complex piecewise cases. You will verify every answer through graphical inspection and numerical approximation. You will gain complete control over the transition points of any real function. This course targets university students and postgraduate researchers in engineering, physics, or mathematics. Advanced secondary school students with strong algebra skills will secure a clear advantage before university entry. Professionals preparing for technical exams will rebuild their analytical foundation. The structured progression and repeated practice ensure that any disciplined learner can apply limit theory to academic or industrial problems.

19 hrs

$ 10.59

Enrolment valid for 12 months
This course is also part of the following learning tracks. You may join a track to gain comprehensive knowledge across related courses.
GET 209: Engineering Mathematics I
GET 209: Engineering Mathematics I
Master the mathematical language of engineering. This programme delivers the complete analytical toolkit required for a successful engineering career, covering single-variable calculus, multivariable calculus, linear algebra, and vector analysis. It provides the essential foundation for all subsequent engineering courses. This programme is for second-year undergraduate students across all engineering disciplines. It delivers the official NUC CCMAS curriculum for Engineering Mathematics, providing the core training required for advanced modules in mechanics, thermodynamics, and circuit theory. Model and analyse complex physical systems using calculus, linear algebra, and vector analysis. You will be equipped to solve problems in dynamics, statics, and field theory, providing the quantitative proficiency required for advanced engineering study and professional practice.

Master the mathematical language of engineering. This programme delivers the complete analytical toolkit required for a successful engineering career, covering single-variable calculus, multivariable calculus, linear algebra, and vector analysis. It provides the essential foundation for all subsequent engineering courses. This programme is for second-year undergraduate students across all engineering disciplines. It delivers the official NUC CCMAS curriculum for Engineering Mathematics, providing the core training required for advanced modules in mechanics, thermodynamics, and circuit theory. Model and analyse complex physical systems using calculus, linear algebra, and vector analysis. You will be equipped to solve problems in dynamics, statics, and field theory, providing the quantitative proficiency required for advanced engineering study and professional practice.

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MTH 201: Mathematical Methods I
MTH 201: Mathematical Methods I
Advanced calculus forms the backbone of engineering, physics, and data science. This track follows the official NUC CCMAS syllabus for MTH 201 to build your mathematical foundation from scratch. You will master real-valued functions, limits, continuity, and differentiability before moving to partial differentiation and multiple integration. The content moves from single-variable theory to multivariable applications used in real-world modelling. Each module uses strict definitions and repeated worked examples to ensure you can solve problems under exam pressure. This is not just theory; it is the practical toolkit required for technical degrees and professional analysis. This programme targets undergraduates in engineering, physical sciences, and mathematics. It suits learners who need to pass MTH 201 with high marks or build a strong base for advanced studies. Secondary school leavers with strong algebra skills can use this track to prepare for university-level rigour. Professionals returning to technical fields will refresh their analytical abilities quickly. If you plan to work in structural design, circuit analysis, fluid dynamics, or economic modelling, this track provides the essential mathematical language you must command. You will analyse domain, range, and behaviour of complex functions without hesitation. You will evaluate limits and prove continuity using formal logical bounds. You will apply differentiation rules, Rolle's theorem, and Taylor series to approximate and optimise systems. You will compute partial derivatives and solve constrained optimisation problems using Lagrange multipliers. You will perform multiple integration over lines, surfaces, and volumes. These skills prepare you for vector calculus, differential equations, and core engineering courses. You will gain the confidence to handle advanced technical coursework and professional modelling tasks with precision.

Advanced calculus forms the backbone of engineering, physics, and data science. This track follows the official NUC CCMAS syllabus for MTH 201 to build your mathematical foundation from scratch. You will master real-valued functions, limits, continuity, and differentiability before moving to partial differentiation and multiple integration. The content moves from single-variable theory to multivariable applications used in real-world modelling. Each module uses strict definitions and repeated worked examples to ensure you can solve problems under exam pressure. This is not just theory; it is the practical toolkit required for technical degrees and professional analysis. This programme targets undergraduates in engineering, physical sciences, and mathematics. It suits learners who need to pass MTH 201 with high marks or build a strong base for advanced studies. Secondary school leavers with strong algebra skills can use this track to prepare for university-level rigour. Professionals returning to technical fields will refresh their analytical abilities quickly. If you plan to work in structural design, circuit analysis, fluid dynamics, or economic modelling, this track provides the essential mathematical language you must command. You will analyse domain, range, and behaviour of complex functions without hesitation. You will evaluate limits and prove continuity using formal logical bounds. You will apply differentiation rules, Rolle's theorem, and Taylor series to approximate and optimise systems. You will compute partial derivatives and solve constrained optimisation problems using Lagrange multipliers. You will perform multiple integration over lines, surfaces, and volumes. These skills prepare you for vector calculus, differential equations, and core engineering courses. You will gain the confidence to handle advanced technical coursework and professional modelling tasks with precision.

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Course Chapters

1. Introduction
2
Meaning of the limits of a real-valued functions - graphical illustrations and formal (epsilon-delta) definitions.
Concept Overviews
2 Lessons
36:46
2. Proving Finite Limits
5
How to prove that a given finite limit as x approaches a finite value is correct, using the formal or epsilon-delta definition.
Problem Walkthroughs
5 Lessons
1:47:01
3. Evaluating Finite Limits (1)
5
Different methods of evaluating limits of real-valued functions - direct substitution, theorems, graphing, factorization, conjugates.
Concept Overviews
5 Lessons
2:03:32
4. Evaluating Finite Limits (2)
4
2
Other methods of evaluating finite limits - L???H??pital???s rule, use of known special limits, squeeze theorem, limits of piecewise-defined functions, etc.
Concept Overviews
4 Lessons
2:09:39
Problem Walkthroughs
2 Lessons
48:24
5. Evaluating Finite Limits (3)
1
2
Intuitive methods of evaluating finite limits of real-valued functions.
Concept Overviews
1 Lesson
45:39
Problem Walkthroughs
2 Lessons
55:23
6. Proving Limits Involving Infinity
2
2
Formal and informal definitions and proofs of limits at infinity and infinite limits.
Concept Overviews
2 Lessons
58:04
Problem Walkthroughs
2 Lessons
1:03:42
7. Evaluating Limits at Infinity
8
3
Different methods of evaluating limits of real-valued functions at infinity and infinite limits.
Concept Overviews
8 Lessons
3:37:34
Problem Walkthroughs
3 Lessons
47:28