Course Description:
Hello there, Engineers, Doctors, Mathematicians, Scientists and Professionals in the making! Welcome to the world of Calculus! Surely you heard a lot of stories about how mind-boggling this subject is! We always have our first impression, right? But before it consume you, set aside worrying derivatives and integration for the meantime. Let this subject fuel you up with imperative knowledge and skills you need to easily deal with Differential and Integral Calculus! Let's prepare ourselves because no one goes into battle unarmed, right?
This course, Precalculus, is a course of study taken as a prerequisite for the study of Calculus. It usually involves branches of Mathematics namely: Advanced Algebra, Analytic Geometry, Number Theory and Trigonometry. During the first part of us being together, we will devote our time on the four non-degenerate conic sections such as: circle, parabola, ellipse, and hyperbola. We will begin with transformational processes and their effects on the equations of the graphs. After establishing its parameters and properties, our discussion on each conic section ends with situational problems. We will end this part by extending the technical skills in finding the point(s) of intersection of two conic sections by solving systems of two nonlinear equations.
On the second part, we will have a thorough discussion of derivation of formulas related to arithmetic and geometric sequences and series. Our discussion is then elevated to general sequences and series, where the introduction of the Principle of Mathematical Induction is inevitable. We will end this part with the proof and applications of the Binomial Theorem.
Finally, before we bid goodbyes and truly say hello to Calculus, we will concentrate on treating trigonometric ratios as functions. It opens with the basic concepts about angles and arcs, their units of measurement. The six trigonometric functions of angles are then defined and explained further through several examples. We will also apply the sine and cosine functions to real-life problems. Moreover, we will explore the analytic treatment of trigonometric functions. It demonstrates several techniques in proving trigonometric identities and solving trigonometric equations. The concept of inverse trigonometric functions is also presented. We will end this course with the introduction of a new coordinate system known as the "polar coordinate system," its relationship to the rectangular coordinate system and its application to real-world situations.
This course, Precalculus, is a course of study taken as a prerequisite for the study of Calculus. It usually involves branches of Mathematics namely: Advanced Algebra, Analytic Geometry, Number Theory and Trigonometry. During the first part of us being together, we will devote our time on the four non-degenerate conic sections such as: circle, parabola, ellipse, and hyperbola. We will begin with transformational processes and their effects on the equations of the graphs. After establishing its parameters and properties, our discussion on each conic section ends with situational problems. We will end this part by extending the technical skills in finding the point(s) of intersection of two conic sections by solving systems of two nonlinear equations.
On the second part, we will have a thorough discussion of derivation of formulas related to arithmetic and geometric sequences and series. Our discussion is then elevated to general sequences and series, where the introduction of the Principle of Mathematical Induction is inevitable. We will end this part with the proof and applications of the Binomial Theorem.
Finally, before we bid goodbyes and truly say hello to Calculus, we will concentrate on treating trigonometric ratios as functions. It opens with the basic concepts about angles and arcs, their units of measurement. The six trigonometric functions of angles are then defined and explained further through several examples. We will also apply the sine and cosine functions to real-life problems. Moreover, we will explore the analytic treatment of trigonometric functions. It demonstrates several techniques in proving trigonometric identities and solving trigonometric equations. The concept of inverse trigonometric functions is also presented. We will end this course with the introduction of a new coordinate system known as the "polar coordinate system," its relationship to the rectangular coordinate system and its application to real-world situations.
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