Foundations Of Physics: Learning Newton's Calculus
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A01=Tengiz Bibilashvili
Accumulation Functions
Algebra to Calculus Transition
Antiderivative
Applied Mathematics Readiness
Approximation Methods
Area Under a Curve
Author_Tengiz Bibilashvili
Average Velocity
Brain Gym Exercises
Bridge Course
Calculus
Calculus Refresher
Calculus Review
Cartesian to Polar Conversion
Category=PBK
Category=PHD
Category=PHU
Chain Rule
Change of Basis
Circular Motion Math Context
Clean Notation Leibniz
Companion for Mechanics
Conceptual Understanding
Constant Acceleration
Constant Velocity
Continuity
Coordinate Geometry
Coordinate Transformations
Cross Product
Definite Integral
Derivative
Determinants
Differential Equations
Differentiation Rules
Displacement and Distance
Dot Product
Engineering Math Prep
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Error-Resistant Methods
Estimation and Checks
Exponential Functions
Exponential Growth and Decay
First Year Calculus
forthcoming
Functions and Graphs
Fundamental Theorem of Calculus
Graphical Interpretation
Historical Notes Context
Indefinite Integral
Initial Value Problems
Integral
Integration by Parts
Integration Techniques
Intuition Building
Kinematics Math Context
Limits
Linear Transformations
Logarithms
Mathematical Modeling
Mathematics for Physics Students
Matrices
Matrix Representation
Multiple Representations
Newton's Calculus
Polar Coordinates
Polar Unit Vectors e_r e_theta
Practice Exercises
Pre-mechanics Mathematics
Preparation for Engineering
Preparation for Upper Division Physics
Problem Solving
Product Rule
Quotient Rule
Radians
Rates of Change
Riemann Sums
Rotation Matrix 2x2
Rotation of Axes
Self-study Friendly
Separable ODEs
Skill Building
Slope
Small-angle Approximation
STEM Preparation
Step-by-Step Derivations
Tangent Line
Teaching Calculus for Physics
Trigonometry
U-substitution
Undergraduate Study Skills
Unit Circle
Unit Vectors
Vector Algebra
Vector Components
Vectors
Worked Examples
Product details
- ISBN 9789819826063
- Publication Date: 28 Aug 2026
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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This book is a mathematical preparation for students about to begin calculus-based mechanics. Its aim is to bridge the gap from basic algebra and trigonometry to the calculus and linear-algebra tools routinely used in first-year physics. Differentiation is developed from tangents and limits to the standard rules; integration is introduced as the inverse of differentiation, grounded in area and Riemann sums. Trigonometry (radians, the unit circle, small-angle approximations, and core identities), vectors and their algebra, basic matrices and coordinate transformations, rotations, polar coordinates, and introductory differential equations (e.g., exponential growth and decay) are presented where they naturally arise in simple mechanics scenarios.The scope is deliberately mathematical: physical examples — constant velocity and acceleration, circular motion, and coordinate changes — serve to illuminate the mathematics rather than to build a full mechanics curriculum. Throughout, the text emphasizes clear reasoning, multiple representations, and tidy derivations supported by worked examples. Exercises, including "Brain Gym" problem sets, promote active engagement and steady skill-building, while brief historical notes and an enthusiastic, direct style invite students to view physics as a living discipline.Designed as a bridge or companion for calculus-based mechanics, this book assumes only algebra and basic trigonometry, and prepares students for subsequent study in physics, engineering, and applied mathematics by cultivating both computational fluency and conceptual clarity.
