Conservation Laws and Applications
Osmotic pressure, chemical potential of water, and membrane water flux
Cell membrane, electrochemical potential of ions, passive transport, and active pumps
Newton’s Law of Viscosity and Non-Newtonian Fluids
What is the Shear Rate in Fluid Mechanics?
The diffusion coefficient and Stokes-Einstein equation
Fick's Second Law of Diffusion
Diffusion from a flat plate into a semi-infinite stagnant medium, diffusion boundary layer thickness
Mass Transfer from a Sphere into a Quiescent Medium
Pharmacokinetics and Drug Delivery Systems
Apparent Volume of Drug Distribution
Drug Metabolism and Renal Excretion
Diffusion-Advection-Reaction Equation
Diffusion and Entropy Maximization & the Arrow of Time
Introduction to Quantum Biology
Quantum Coherence and Photosynthesis
Quantum Vibration and Olfaction
Quantum Entanglement and Magnetoreception
The High Fidelity of DNA Replication
Ion Transport and Consciousness
Implications of Synthetic Biology
Classical Physics: Features, Scope, and Limitations
At What Scales Does Quantum Physics Play a Role?
The Schrödinger Equation and Its Statistical Interpretation
Normalization of the Wave Function
Stationary States and Quantization of Energy
Expectation Values and Operators of Position and Momentum
The Bra and Ket Notation in Quantum Physics
Orthonormal Bases and Quantum State Representation
Quantum States and Their Representations
Observables in Quantum Physics
The Commutator and the Uncertainty Principle
Pure versus Mixed Quantum States
Density Operators in Quantum Physics
Angular Momentum in Quantum Physics
What is Spin in Quantum Physics?
Magnetic Dipole Moment and Spin Angular Momentum
Bloch Representation of Quantum States
Radical Pairs: Formation, Behavior, and Reactions
Time-Dependent Expectation Values and Constants of Motion
Tensor Product: Theory and Applications
Applying Operators on Tensor Products
Quantum Phases and Their Significance
Quantum Coherence and Decoherence
Fermi's Golden Rule on Quantum Transition Rates
Raising and Lowering Operators
Time Evolution of Quantum Operators
Quantum Mechanics of the Hydrogen Bond
Biological Scales: From Molecules to Ecosystems
G-Proteins and G-Protein Coupled Receptors
A Classical Model of DNA Stability
Mathematical Modeling of Neural Signaling
Discrete Random Variables: Expectation, Variance, and Standard Deviation
Continuous Random Variables: Expectation, Variance, and Standard Deviation
Understanding the Funding Agency’s Goals
Clearly Define Research Questions and Objectives
Literature Review and Theoretical Framework
Research Proposal Methodology & Design
Proposal Budgeting and Financial Planning
Craft Strong Significance and Impact in Research Proposals
Risk Management and Alternative Approaches
Creating a Research Proposal Timeline
Building a Strong Research Team
Ethics, Compliance, and Data Management
Writing Style and Proposal Structure
Sustaining Research Beyond the Grant
Review and Refine Your Research Proposal
Research Paper Topic Selection: Clarity and Relevance
Mastering the Literature Review
Crafting a Research Question or Hypothesis
Research Methodology for Academic Writing
Data Presentation and Analysis
Crafting a Captivating Introduction
The Power of Simplicity and Visual Design
Designing Effective Visual Cues for Presentations
Color Contrast: Science and Perception
Font Style and Mood: The Power of Typography
Presentation Mastery: The Power of White Space
Using Pictures to Evoke Emotion
Engaging Your Audience: Eight Presentation Tips
Designing Effective Poster Presentations
How to Engage Your Audience Through a Poster Presentation
Mastering Body Language in Presentations
Crafting Compelling Narratives
Effective Highlighting in Presentations
Mastering Voice Control and Tone in Presentations
Presentation Structures and Formats
Conquer Presentation Nervousness
Mastering Presentation Openings, Closings, and Transitions
Handling Questions and Difficult Audiences with Confidence
Persuasion and Influence in Presentations
Mastering Virtual Presentations
Designing with Proximity: Stronger Presentations
The Principle of Closure in Presentation Design
Mastering Connection: Revolutionizing Communication
Mitigating Cognitive Bias for Professional and Personal Growth
Derivatives, gradients, and their applications to machine learning
Introduction to Differential Equations
Solving Partial Differential Equations via Separation of Variables
Initial and Boundary Conditions in Differential Equations
Error Function and the Complementary Error Function
The Dirac Delta Function and the Fourier Transform
Vector Spaces and Their Applications
Inner Product Spaces: Theory and Applications
Dual Vector Spaces and Their Applications
Projection Matrices and Their Applications
Geometric Interpretation of Matrices
Understanding Matrix Rank, Null Spaces, and Their Perpendicular Properties
Symmetry, Involutory, Unitary, and Hermitian Matrices
Linear Independence and Dependence
Invariance of the Trace of a Matrix
The Truth About Learning: Why Reading Alone Isn’t Enough
Unlocking the Mysteries of Calculus & Differential Equations: A Guide for Struggling Students
The Power of Neuroplasticity in Learning
Ace Your Finals: The Night Before Edition (STEM Focus)
Brain Freeze: Overcoming Exam Stress in STEM
Spaced Learning: The Ultimate Guide to Effective Studying
Mastering Note-Taking for Academic Success
Building Resilience: Traits, Steps, and Mindset
Mastering Time Management for Success
Unlocking Your Potential: A Growth Mindset
Cultivating Self-Awareness for Personal Growth
Building a Strong Foundation: Developing Your Core Values
Mastering Emotional Intelligence: The Key to Personal and Professional Success
The Science of Habit Formation
Mindset Mastery: Overcoming Limiting Beliefs
The Power of Repetition: Unlocking Consistency for Success
Master Your Mind: How to Stay Focused