A conceptual approach for students interest in theoretical foundations of mathematics. Attention is given to computational aspects as well as problem-solving techniques. Limits and continuity, mean value theorem, elementary transcendental functions including trigonometric functions, inverse function theorem, differentiation, integration, fundamental theorem of calculus, Taylor's theorem, sequences and series, power series, and applications. This course will be useful for students interested in learning theoretical calculus and proofs in relation to future studies in computer science, economics, mathematics, physics, and statistics.